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Applications of Integrals: Arc Length: Example 3: Simpson's Rule Approximation

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First published at 17:55 UTC on May 8th, 2019.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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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://1drv.ms/x/s!As32ynv0LoaIhqY0hUhbEoGq14X_lg?e=JOOLQF

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 .

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