Explanation Given: y = x 3 2 , [ 1 , 2 ] Key Concept and Formula Used: The arc length s of function y = f ( x ) over [ a , b ] is equal to s = ∫ a b 1 + ( f ' ( x ) ) 2 d x d d x x n = n x n − 1 and ∫ x n d x = x n + 1 n + 1 + C Calculation: To calculate the arc length we first differentiate the given function and then use the formula to find the arc length. y = x 3 2 = f ( x ) f ' ( x ) = d d x ( x ) 3 2 = 3 2 ( x ) 3 2 − 1 = 3 2 x 1 2 Arc length= s = ∫ a b 1 + ( f ' ( x ) ) 2 d x where a = 1 & b = 2 s = ∫ 1 2 1 + ( 3 2 x 1 2 ) 2 d x = ∫ 1 2 1 + 9 4 x d x = ∫ 1 2 4 + 9 x 4 d x s = 1 2 ∫ 1 2 9 x + 4 d x ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9.1, Problem 7E

To determine

the arc length over the given interval.

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Chapter 9.1, Problem 6E

Chapter 9.1, Problem 8E

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Chapter 9 Solutions

Calculus - Standalone book

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the arc length over the given interval.

Solution Summary: The arc length of function y = f (x) over [a, b] is equal to s = 2 d x

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the arc length over the given interval.

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Chapter 9 Solutions