8.1 Arc Length Question #4 (Medium)
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8.1 Challenging Integral Applications
Question #4 (Medium): Arc Length Approximation Using Simpson’s Rule
For functions where evaluating
is challenging, Simpson’s Rule can be used
to approximate the length of the curve for the given interval. As a review, Simpson’s Rule follows:
where is even and
Using Simpson’s Rule with , estimate the length of the curve. Then compare the answer to the
value produced by the calculator.
First, taking the derivative of the function.
. From here in order to apply the Simpson’s Rule which
approximates the area under the curve, we can let
Based on computer calculation of the integral:
. So we can see that
Simpson’s rule gives a very lose approximation.
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