This

**preview**shows half of the first page. to view the full**1 pages of the document.**8.1 Challenging Integral Applications

Arc Length

Question #4 (Medium): Arc Length Approximation Using Simpson’s Rule

Strategy:

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

.

Sample Question:

Using Simpson’s Rule with , estimate the length of the curve. Then compare the answer to the

value produced by the calculator.

,

Solution:

First, taking the derivative of the function.

. Thus,

. From here in order to apply the Simpson’s Rule which

approximates the area under the curve, we can let

.

.

Then:

Based on computer calculation of the integral:

. So we can see that

Simpson’s rule gives a very lose approximation.

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