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Parametric Calculus: Surface Area Part 1

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First published at 21:50 UTC on October 8th, 2017.

Math Easy Solutions

MES

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In this video I go over further into the wonderful world of calculus with parametric curves and this time go over part 1 of the proof for the formula for the surface area of a shape formed by rotating a curve about the x-axis. In part 1 I look at the case where the parametric equations can also be written as a typical function, y = F(x), which is the same as the surface area proof that I covered in my earlier video. In this case, we can simply use the substitution rule for definite integrals to change the basic surface area integral formula to one that accounts for the extra parametric parameter, just as in my earlier videos on arc length for parametric curves. Also just like for arc length, this formula derived using substitution is also valid even if the parametric equations can’t be written in the form of y = F(x) (i.e. a one-to-one function). I will illustrate this in part 2 by using polygonal approximation, again just like as for arc length, so stay tuned for that video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuVHlucbBJUJvLRNDA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-surface-area-part-1

Related Videos:

Parametric Calculus: Arc Length Part 3 (Debunking My Own Video): https://youtu.be/udz4jzUgPBg
Parametric Calculus: Arc Length Part 2: https://youtu.be/anD_j0nDDPA
Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ
Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM
Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
The Substitution Rule for Definite Integrals: http://youtu.be/AzmYfV1vsbU .

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