Math Easy Solutions

Math Easy Solutions

MES

subscribers

In this video I go over an example on using the Arc Length formula to determine the length of a curve and this time determine the length of the curve y^2 = x^3 from between the points (1, 1) and (4, 8). I also show how we can double check our answer by noticing that the function is only slightly curved and so the distance between the two points should be just slightly smaller than the length of the curve. This is an important example in illustrating the arc length concept so make sure to watch it!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103169&authkey=!AKGxv4AaftK2Y-M&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-example-1

Related Videos:

Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
The Substitution Rule for Definite Integrals: Examples: http://youtu.be/CGzWQXTZtog .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on using the arc length formula to determine the length of the curve and this time show that it is sometimes easier to deal with x as a function of y, i.e. x = f(y), instead of the typical y = f(x) that we are accustomed to. This is especially the case in this example in which I solve for the length of the curve y^2 = x from the points (0, 0) to (1, 1). Since we are given the function already in terms of x = f(y) it is easier working with this function as opposed to dealing with a square root as in y = +/- sqr(x). When dealing with the function this way, we can still use the arc length formula, but we just have to simply switch the variables.

This is a very useful example because it illustrates how sometimes it is easier to deal with x as a function of y, as well as showing how the square root that appears in the arc length formula usually leads to very difficult or even impossible integrals to explicitly evaluate, as I will show in my next video.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103189&authkey=!ADrDTOz4ca15ggI&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-example-2-x-f-y

Related Videos:

Applications of Integrals: Arc Length: Example 1: https://youtu.be/Fqp2ai2RBEE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Trigonometric Integrals: Example 8: sec(x)^3: http://youtu.be/6381DXW85kA
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the proof of the trigonometry identity tan^2(x) + 1 = sec^2(x). The proof of this identity is very simple and like many other trig identities, stems from the basic trig identity, known as the Pythagorean trig identity: sin^2(x) + cos^2(x) = 1 (the proof of this identity is shown in the related videos below). The derivation of identity is to simply divide the Pythagorean trig identity by cos^2(x) on both sides and use the definitions of tan(x) and sec(x) to re-write the resulting identity.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103202&authkey=!AKS2Cx-58iguxv0&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometry-identity-tan-2-x-1-sec-2-x

Related Videos:

Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM
Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
Trigonometric Identity: cos(2x) = 1 - 2sin^2(x): http://youtu.be/XGk2CpbEl8I
Trigonometry Identity: tan(-x) = tan(x): http://youtu.be/nvaP_091Ar8
Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI
Trigonometry: Product Identities: http://youtu.be/os8XKWAj9P8
Trigonometric Identity: sin(π-x) = sin(x): http://youtu.be/x36tRrVGtX0 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the proof of another trigonometry identity and this time prove the identity: 1 + cot^2(x) = csc^2(x). The proof for this is similar to the identity proof in my last video, and involves simply dividing both sides of the basic Pythagorean Identity sin^2(x) + cos^2(x) = 1 by sin^2(x) instead of by cos^2(x) as I did in my last video.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103209&authkey=!AN2Ybn1ab-sMNgc&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometry-identity-1-cot-2-x-csc-2-x

Related Videos:

Trigonometry Identity: tan^2(x) + 1 = sec^2(x): https://youtu.be/5i3NZ_xip7I

Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM
Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
Trigonometric Identity: cos(2x) = 1 - 2sin^2(x): http://youtu.be/XGk2CpbEl8I
Trigonometry Identity: tan(-x) = tan(x): http://youtu.be/nvaP_091Ar8
Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI
Trigonometry: Product Identities: http://youtu.be/os8XKWAj9P8
Trigonometric Identity: sin(π-x) = sin(x): http://youtu.be/x36tRrVGtX0 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on determining the arc length of a curve and this time use Simpson's Rule to estimate the arc length of the curve xy = 1 from the points (1, 1) to (2, 1/2). This is a very interesting example in that it shows that the resulting integral when using the arc length formula sometimes is very difficult to evaluate because of the appearance of the square root. So instead of trying to solve for this integral explicitly, we instead estimate it using the Simpson's Rule with n = 10 subintervals and come up with a pretty accurate, up to 4 decimal places, estimation.

Download the notes in my video:

Notes: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103219&authkey=!AIzLLy3HSflC_LM&ithint=file%2cpdf
Excel Notes: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103220&authkey=!AHQJQUWhPHH7ATM&ithint=file%2cxlsx

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-example-3-simpson-s-rule-approximation

Related Videos:

Applications of Integrals: Arc Length: Example 2: x = f(y): https://youtu.be/07Peo5ms848
Applications of Integrals: Arc Length: Example 1: https://youtu.be/Fqp2ai2RBEE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over further into the Arc Length Formula and this time explain how it is sometimes useful to have a function that measures the arc length of a curve from a particular starting point point to any other point on the curve. From the arc length formula we determine this function, which is called the Arc Length Function. Also in this video, I write the integrand of the arc length formula in terms of differentials in order to develop a useful visual geometric interpretation of the rate of change of arc length. This is a very interesting video on arc length so make sure to watch this video!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103234&authkey=!ACz4krW757H4JjE&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-function

Related Videos:

Applications of Integrals: Arc Length: Example 3: Simpson's Rule Approximation: https://youtu.be/7x6-t0Nebxw
Applications of Integrals: Arc Length: Example 2: x = f(y): https://youtu.be/07Peo5ms848
Applications of Integrals: Arc Length: Example 1: https://youtu.be/Fqp2ai2RBEE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Differentials Notation in Linear Approximation: http://youtu.be/s0adatWiZg4
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a pretty extensive example on determining the arc length of a curve but this time determine it as a function of x. This allows the ability to measure the length of a curve from a given point up to any point on the curve. The arc length function in this example is determined for the curve y = x^2 - 1/8*ln(x) from the starting point (1, 1).

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103260&authkey=!AMedjB8y_xVwSeY&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-example-4-arc-length-function

Related Videos:

Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length: Example 3: Simpson's Rule Approximation: https://youtu.be/7x6-t0Nebxw
Applications of Integrals: Arc Length: Example 2: x = f(y): https://youtu.be/07Peo5ms848
Applications of Integrals: Arc Length: Example 1: https://youtu.be/Fqp2ai2RBEE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ
Derivative of y = Log(x) and y = Ln(x): http://youtu.be/5e6MisvvMPE .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the proof of the integral of the trigonometric function cos^2(x) and show that it is equal to 1/2*(x + sin(x)cos(x)) + C. In evaluating this integral I show that it is easier to evaluate if we can get rid of the square power, which is possible when using the half angle trig identity: cos^2(x) = 1/2*(1 + cos(2x).

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103306&authkey=!AHrEezPMe5bRpdM&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-integrals-integral-of-cos-2-x

Related Videos:

Trigonometric Integrals: Example 1: http://youtu.be/UO0DjuF4330
Trigonometric Integrals: Example 2: http://youtu.be/0Omohf0WbbU
Trigonometric Integrals: Example 3: sin(x)^2: http://youtu.be/-sLS4uBoq5M
Trigonometric Integrals: Example 4: sin(x)^4: http://youtu.be/vf_Vk8teH9E
Trigonometric Integrals: Guidelines for sin(x)cos(x): http://youtu.be/aE8Sz5BdMT8
Trigonometric Integrals: Example 5: http://youtu.be/Rfel0uY5H1Y
Trigonometric Integrals Example 6 : http://youtu.be/Ll9j-ZUgrmo
Trigonometric Integrals: Guidelines for tan(x)cos(x): http://youtu.be/oz5nXlYQPB0
Trigonometric Integrals: Example 7: tan(x)^3: http://youtu.be/kFaj0djxfak
Trigonometric Integrals: Example 8: sec(x)^3: http://youtu.be/6381DXW85kA
Trigonometric Integrals Example 9: sin(4x)cos(5x): http://youtu.be/2cLOj0549rw
Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another trig integral and this time show that the integral of the trig function sin^2(x) is 1/2*(x - sin(x)cos(x)) + C. The method in evaluating this integral is very similar to my last video on the integral of cos^2(x). Basically this integral is evaluated by first removing the square power by using a half-angle trig identity and then using the trig identity sin(2x) = 2*sin(x)cos(x) to further simplify the integral.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103334&authkey=!AKtP3HB8EQqnys0&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-integrals-integral-of-sin-2-x

Related Videos:

Trigonometric Integrals: Integral of cos^2(x): https://youtu.be/uuWIDgQ8NsY
Trigonometric Integrals: Example 1: http://youtu.be/UO0DjuF4330
Trigonometric Integrals: Example 2: http://youtu.be/0Omohf0WbbU
Trigonometric Integrals: Example 3: sin(x)^2: http://youtu.be/-sLS4uBoq5M
Trigonometric Integrals: Example 4: sin(x)^4: http://youtu.be/vf_Vk8teH9E
Trigonometric Integrals: Guidelines for sin(x)cos(x): http://youtu.be/aE8Sz5BdMT8
Trigonometric Integrals: Example 5: http://youtu.be/Rfel0uY5H1Y
Trigonometric Integrals Example 6 : http://youtu.be/Ll9j-ZUgrmo
Trigonometric Integrals: Guidelines for tan(x)cos(x): http://youtu.be/oz5nXlYQPB0
Trigonometric Integrals: Example 7: tan(x)^3: http://youtu.be/kFaj0djxfak
Trigonometric Integrals: Example 8: sec(x)^3: http://youtu.be/6381DXW85kA
Trigonometric Integrals Example 9: sin(4x)cos(5x): http://youtu.be/2cLOj0549rw
Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
Half Angle Trigonometry Identities: http://youtu.be/0bY6tHZhBSI .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a pretty useful example on the area of a surface formed by rotating an arc on the circle x^2 + y^2 = 4 from x = -1 to x = 1 about the x-axis. The resulting shape is part of a sphere and I use the formula for surface area developed in my last video to evaluate it. This is a useful video on illustrating how to go about solving surface area so make sure to watch it!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103594&authkey=!AHpO5MRBC1IpnXc&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-1

Related Videos:

Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a pretty extensive and in-depth video in proving that the area of a sector of a circle is equal to 1/2 r^2*θ. This formula works for any angle in the circle. The proof involves first considering a sector that is at most a quarter of a large circle and breaking it into two areas: a triangle and a curved section. The area of the curved section requires trigonometric substitution for integrals and as well as a good understanding of trigonometric functions in general to evaluate. Although this video is almost an hour long, it brings together many different concepts of mathematics in finally deriving a very short and concise formula for the area of a sector of a circle, thus this video is a important video to watch!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103419&authkey=!ADTcnCJDE-RQbwk&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/area-of-a-sector-of-a-circle-proof

Related Videos:

Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw
Inverse Trigonometric Functions: Inverse cosine, sine, and tan Functions: http://youtu.be/Ifv1vkJZdrk
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo
Trigonometric Substitution for Integrals: One to One Function: http://youtu.be/QO26MkCC3eU
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Trigonometric Integrals: Integral of cos^2(x): https://youtu.be/uuWIDgQ8NsY

Download the notes in my video:

Related Videos: .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the trig identities for sin^2(-x), cos^2(-x), and tan^2(-x) and show that they are equal to sin^2(x), cos^2(x), and tan^2(x), respectively. This means that the values are the same whether x is positive or negative. This also means that the functions are all "even" functions as well as being symmetric about the y-axis. The proof for these identities is pretty straight forward and involves using the basic trig identities: sin(-x) = - sin(x) and cos(-x) = cos(x).

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103347&authkey=!AD4CvzcE8mRuS60&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/trigonometric-identities-sin-2-x-cos-2-x-tan-2-x

Related Videos:

Trigonometry Identity: tan^2(x) + 1 = sec^2(x): https://youtu.be/5i3NZ_xip7I
Trigonometry Identity: 1 + cot^2(x) = csc^2(x): https://youtu.be/tFKQfOTekoI
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Trigonometry Graphing: Sin, Cos, Tan Functions: http://youtu.be/l_3cgeq-YXE
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the concept of determining the area of a surface of a general shape as we rotate it about an axis. The derivation is very similar to my earlier derivations of the length of a curve, and the volume of a shape formed as you rotate it about a curve. In this derivation, I use the length of a curve formula to first determine the length of a small section of a curve, and then rotate that curve about an axis to determine the surface area. Then I make the length very small and sum up to an infinite amount of small sections or bands which form the shape and thus we can write the surface area as an integral. This is a very extensive derivation video but it puts together many of the concepts of integrals and infinite sums so make sure to watch it!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103547&authkey=!AObmWwIhmH8v7VU&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area

Related Videos:

Area of a Sector of a Circle: Proof: https://youtu.be/lglnySF8DyY
Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk
Integrals and Areas Between Curves: Functions of y: http://youtu.be/gqXUD27NTkI
Integrals and Volumes: http://youtu.be/-evdvkDwBuQ
Integrals and Volumes by Cylindrical Shells: http://youtu.be/LbywV9X154E
The Definite Integral and Riemann Sums: Introduction : http://youtu.be/vhMP5SKbQjU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on determining the area of a surface obtained by rotating a curve about an axis. In this example, I calculate the surface area of a shape formed by rotating the arc of the parabola y = x^2 from the point (1, 1) to (2, 4) about the y-axis. As a check of the answer obtained, I calculate the shape of a cylinder as well as a frustum of a cone that is similar to the shape we are trying to calculate, thus the resulting surface areas should all be similar as well.

The solution I use in this video uses the surface area formula in which the arc length is written using dx as opposed to dy. In my next video I solve this same example using dy in the arc length formula instead so stay tuned for that video!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103605&authkey=!AMWD5-Q4RS1QsQo&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-2-solution-1

Related Videos:

Applications of Integrals: Surface Area: Example 1: https://youtu.be/E9rwIVUifuA
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the same example as in the last video surface area but this time write the resulting surface area integral in terms of y and dy as opposed to x and dx. This is possible because the arc length can be written in either notation and thus the resulting integral and final answer is the same.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103729&authkey=!AAhYJ6Jugs1t1yk&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-2-solution-2

Related Videos:

Applications of Integrals: Surface Area: Example 2: Solution 1: https://youtu.be/5nUzb02pDcI
Applications of Integrals: Surface Area: Example 1: https://youtu.be/E9rwIVUifuA
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on determining the surface area of a shape formed by rotating a curve about an axis. In this case I determine the surface area of the shape formed by rotating the curve, y = e^x, from x = 0 to x = 1 about the x-axis. Like in my earlier videos, I explain how we can solve this surface area by either writing the surface area formula in terms of x or in terms of y. In this example, I solve it in terms of x (solution 1) and in the next video I will solve it in terms of y (solution 2). This is a pretty extensive example, but it helps to illustrate the many steps that are often required, so make sure to watch this video!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104244&authkey=!AF3xM2tK3lNLxHk&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-3-solution-1

Related Videos:

Applications of Integrals: Surface Area: Example 2: Solution 2: https://youtu.be/nlL8ePAYT50
Applications of Integrals: Surface Area: Example 2: Solution 1: https://youtu.be/5nUzb02pDcI
Applications of Integrals: Surface Area: Example 1: https://youtu.be/E9rwIVUifuA
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Trigonometric Integrals: Example 8: sec(x)^3: http://youtu.be/6381DXW85kA
Trigonometry Identity: tan^2(x) + 1 = sec^2(x): https://youtu.be/5i3NZ_xip7I
Trigonometric Substitution for Integrals: One to One Function: http://youtu.be/QO26MkCC3eU .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the same example 3 on surface area which I covered in my last video but this time solve it by writing the integral in terms of x, solution 2, as opposed to solution 1 which was in terms of y. In this particular example writing the integral in terms of y skips the need to use the initial substitution for integrals technique which I covered in my last video. But the rest of the solution is the same as that in my last video, which is why I skipped the full derivation of this integral, so make sure to watch my last video as well!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104262&authkey=!AAARjidnQLM3M0M&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-surface-area-example-3-solution-2

Related Videos:

Applications of Integrals: Surface Area: Example 3: Solution 1: https://youtu.be/I6PuKsxwyow
Applications of Integrals: Surface Area: Example 2: Solution 2: https://youtu.be/nlL8ePAYT50
Applications of Integrals: Surface Area: Example 2: Solution 1: https://youtu.be/5nUzb02pDcI
Applications of Integrals: Surface Area: Example 1: https://youtu.be/E9rwIVUifuA
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Graph of Natural Logarithm y = ln(x): http://youtu.be/GZkwYVdbluc .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I revisit my earlier proof of the area of a sector of a circle, and this time show how it can be solved using only definite integrals. In my earlier proof video I used an indefinite integral method to solve the step that involved trig substitution for integrals because I did not want to change the intervals of integration. But in this video using only definite integrals provides a useful concept to understand, which is always keeping track of the variables being used or substituted. Thus by using the definite integral method, I show how the angle I am substituting is different than the actual angle of the sector of the circle that I am deriving the area for. This is a pretty interesting and useful video on understanding the importance of the intervals of integration so make sure to watch this video!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104271&authkey=!AND6pxQG88tEyDo&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/area-of-a-sector-of-a-circle-revisited-using-definite-integrals-only

Related Videos:

Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: http://youtu.be/ln03a5KvQAY
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw
Inverse Trigonometric Functions: Inverse cosine, sine, and tan Functions: http://youtu.be/Ifv1vkJZdrk
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry Identities: cos(2π + x), sin(2π + x), cos(π/2 -x), sin(π/2 -x): http://youtu.be/EynSefQs308
Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo
Trigonometric Substitution for Integrals: One to One Function: http://youtu.be/QO26MkCC3eU
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Trigonometric Integrals: Integral of cos^2(x): https://youtu.be/uuWIDgQ8NsY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I prove that the sum of the angles in any 4-sided polygon, known as a quadrilateral, is equal to 360 degrees. I prove it using two methods. The first method involves drawing parallel lines about 1 point and showing how all the angles add up to form a full revolution, which in turn is by definition equal to 360 degrees. The second proof uses the fact that the sum of the angles in any triangle add up to 180 degrees. Thus by splitting the quadrilateral into 2 triangles, we can then sum all the angles to equal to 180 + 180 which is simply 360 degrees. This is a very useful and interesting video on angles and using parallel lines to determine the corresponding angles so make sure to watch this video!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104289&authkey=!AGhtVMBr70_6aGM&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/sum-of-angles-in-4-sided-polygon-proof

Related Videos:

Proof that Sum of Angles in ANY Triangle = 180 degrees: http://youtu.be/4bI3BXIe2k8
Angles - Degrees vs Radians: What are Radians??: http://youtu.be/bOdrVvQWRdE .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another very interesting discovery project, which is a series of advanced math concepts at the end of each chapter in my calculus textbook. This discovery project involves working the area, surface area, and volume of a shape that is rotated on a slanted line, as opposed to the typical vertical and horizontal lines which I covered before. I solve question 1 in this video, which involves determining the area of the region with respect to the slanted line. The solution to this video involves using trigonometry to write the terms on the slanted line in terms of x. This is a very interesting video so make sure to watch it and stay tuned for more on this project in my later videos!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104297&authkey=!AGZErrrmhurKIX0&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematic/@mes/applications-of-integrals-discovery-project-rotating-on-a-slant-question-1

Related Videos:

Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)): http://youtu.be/uQUu0XFMw8I
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6: http://youtu.be/XgE75Pa0n-c
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
General Area of a Region Definition/Formula: http://youtu.be/_k1NWSF_pl0
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Proof that Sum of Angles in ANY Triangle = 180 degrees: http://youtu.be/4bI3BXIe2k8 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I continue further in the Discovery Project series which I started in my last video. In this video I use the derivation of the area of a region below a curve but above a slanted line, which I solved in my last video, to solve for an area with a known function and slanted line. In this video I solve for the area of the region bounded by the curve y = x + sin(x) and the slanted line y = x - 2. This is a useful example on using the formula for the area so make sure to watch it and stay tuned for more on this Discovery Project series!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104333&authkey=!AFHtmB2n9oYR2rM&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-discovery-project-rotating-on-a-slant-question-2

Related Videos:

Discovery Project: Rotating on a Slant: Question 1: https://youtu.be/dXlhpDOBDe0
Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)): http://youtu.be/uQUu0XFMw8I
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6: http://youtu.be/XgE75Pa0n-c
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk
Derivative of Trigonometry Functions: Derivative of cos(x): http://youtu.be/LMjVp-GsrCw
Properties of Definite Integrals - Part 1: http://youtu.be/XAel-Zti_Hs
Properties of Definite Integrals - Part 2: http://youtu.be/lxkQmB11qoU
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over question 3 on the Discovery Project: Rotating on a Slant video series. This time I derive the general formula for the volume of a shape generated by rotating a curve about a slanted line. I use the derivation I made earlier in Question 1 for the area of the region between the curve and the slanted line to solve for the volume. The volume equation I derive is very similar to that for the area but involves squaring the radius of revolution. To understand this question in detail, make sure to watch the first questions of this video series!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104360&authkey=!ABktqgP4-ovLXSE&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-discovery-project-rotating-on-a-slant-question-3

Related Videos:

Discovery Project: Rotating on a Slant: Question 3: https://youtu.be/zwodt1OsFjE
Discovery Project: Rotating on a Slant: Question 1: https://youtu.be/dXlhpDOBDe0
Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)): http://youtu.be/uQUu0XFMw8I
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6: http://youtu.be/XgE75Pa0n-c
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
Integrals and Volumes: http://youtu.be/-evdvkDwBuQ .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over Question 5 of the Discovery Project: Rotating on a Slant video series. In this question, I derive the surface area formula of the shape generated by rotating the curve about a slanted line. The derivation is fairly easy because the majority of the work was in Question 1 when the variables on the slanted line were rotated to write in terms of x.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104392&authkey=!AM7ZI568EbxWse0&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/discovery-project-rotating-on-a-slant-question-5

Related Videos:

Discovery Project: Rotating on a Slant: Question 4: https://youtu.be/w3eR3d-dJRI
Discovery Project: Rotating on a Slant: Question 3: https://youtu.be/zwodt1OsFjE
Discovery Project: Rotating on a Slant: Question 3: https://youtu.be/zwodt1OsFjE
Discovery Project: Rotating on a Slant: Question 1: https://youtu.be/dXlhpDOBDe0
Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)): http://youtu.be/uQUu0XFMw8I
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6: http://youtu.be/XgE75Pa0n-c
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
Google Plus: https://mes.fm/gplus
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over Question 6 of the Discovery Project: Rotating on a Slant video series. This question involves using the surface area formula derived in question 5 to evaluate the area of the surface generated by rotating the curve y = sqrt(x) from x = 0 to x = 4 about the slanted line y = 1/2*x. The resulting integral is very complicated to solve by hand so instead I use an online integral calculator, which uses a computer algebra system (CAS), to symbolically solve the integral as well as evaluate it. This is a very interesting video as it shows just how complex integrals can get simply because we rotate about a slanted line as opposed to a vertical or horizontal line. Also, the majority of the video is just me showing how to use algebra and logarithmic properties to make the answer given by the integral calculator match the answer given in my calculus book.

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104405&authkey=!AJELQp69Eo2h0WQ&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/discovery-project-rotating-on-a-slant-question-6

Related Videos:

Discovery Project: Rotating on a Slant: Question 5: https://youtu.be/6c_4v9JeFsI
Discovery Project: Rotating on a Slant: Question 4: https://youtu.be/w3eR3d-dJRI
Discovery Project: Rotating on a Slant: Question 3: https://youtu.be/zwodt1OsFjE
Discovery Project: Rotating on a Slant: Question 3: https://youtu.be/zwodt1OsFjE
Discovery Project: Rotating on a Slant: Question 1: https://youtu.be/dXlhpDOBDe0
Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)): http://youtu.be/uQUu0XFMw8I
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6: http://youtu.be/XgE75Pa0n-c
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
Google Plus: https://mes.fm/gplus
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over further into applications of integrals and this time go into the field of physics and engineering by going over an introduction on Hydrostatic Pressure and Force. When you go swimming, you will notice that the deeper you go the more pressure or force you will feel acting on you. This is because the deeper you go, the more water is above you, thus adding its weight on top of you. From this weight we can define the force and pressure acting on you, either in SI units or U.S. Imperial units. Another important concept to understand about this hydrostatic pressure, is that the pressure is the same in any direction at any given point underwater. This is an experimentally proven fact and is very useful in hydro-engineering.

Another important note, which I forgot to mention in the video, is that the force due to water is called hydrostatic because the word "hydro" is identified with water, and the word "static" shows the force we are dealing with is when the water or other type of fluid is at a static or non-moving phase.

This is a very important introduction to a very large and important engineering field, so make sure to watch it! In later videos I will go over how to apply integrals and integration in solving for the hydrostatic force and pressure so stay tuned!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104458&authkey=!ACrVe5vhzfG0S74&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-hydrostatic-pressure-and-force

Related Videos:

Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Simplified Filter Criteria: A Dam Filter Example: http://youtu.be/yGEeYAb4Olw
Soil Mechanics 101 - Phase Relations: http://youtu.be/DtKheQcL2BU
Types of Tailings Embankments: Upstream, Downstream and Centerline Construction Methods: http://youtu.be/1wm1XR6z-QE
Buoyancy - What is Archimedes' Principle and it's Proof: http://youtu.be/mXzccaH2KNI .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
Google Plus: https://mes.fm/gplus
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

SHOW MORE

Created 1 year, 8 months ago.

380 videos

CategoryEducation

I mainly teach math, but also do controversial videos that are censored on YouTube, as well as creating #FreeEnergy technology!