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Lecture

# 8.1 Arc Length Question #4 (Medium)

Department
Mathematics
Course Code
MAT136H1
Professor
all

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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.