Explanation Given: y = ln ( c o s x ) , [ 0 , π 4 ] 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 , d d x cos x = − sin x , d d x sin x = cos x , log 1 = 0 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 = ln ( c o s x ) = f ( x ) f ' ( x ) = d d x [ ln ( c o s x ) ] = 1 cos x d d x cos x = − sin x cos x = − tan x Arc length=

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9.1, Problem 10E

To determine

the arc length over the given interval.

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Chapter 9.1, Problem 9E

Chapter 9.1, Problem 11E

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Chapter 9 Solutions

Calculus - Standalone book

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the arc length over the given interval.

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Chapter 9 Solutions