Explanation Given: y = 1 4 x 2 − 1 2 ln x , [ 1 , 2 e ] 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 , ∫ 1 x d x = ln x + C 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 = 1 4 x 2 − 1 2 ln x = f ( x ) f ' ( x ) = d d x [ 1 4 x 2 − 1 2 ln x ] = 1 4 × 2 x − 1 2 x = x 2 − 1 2 x Arc length= s = ∫ a b 1 + ( f ' ( x ) ) 2 d x where a = 1 & b = 2 e s = ∫ 1 2 e 1 + ( x 2 − 1 2 x ) 2 d x = ∫ 1 2 e 1 + (

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.2, Problem 9E

To determine

the arc length over the given interval.

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Chapter 9.2, Problem 8E

Chapter 9.2, Problem 10E

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Chapter 9 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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