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Lecture

# 8.1 Arc Length Question #4 (Medium)

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School
University of Toronto St. George
Department
Mathematics
Course
MAT136H1
Professor
all
Semester
Winter

Description
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, ∫ √ ( ) √ √ ∫ √ ( ) ∫ √ .
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