Explanation Given information: The given function is y = ln ( sin x ) and the interval is [ π 4 , π 2 ] . Formula used: Assume that f ( x ) ≥ 0 and f ′ exists and continuous on the interval [ a , b ] . The arc length over the interval is given by L = ∫ a b 1 + [ f ′ ( x ) ] 2 d x The formula of the integral of sec x is shown below. ∫ cos e c x d x = ln | cos e c x − cot x | + c Calculation: Consider the given function. y = f ( x ) = ln ( sin x ) Differentiate the above function with respect to x . f ′ ( x ) = 1 sin x d d x ( sin x ) = cos x sin x = cot x The given interval is [ π 4 , π 2 ] . Here, a = π 4 , b = π 2 For π 4 ≤ x ≤ π 2 , x ≥ 0 and f ′ exists and continuous on [ π 4 , π 2 ]

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 8.2, Problem 31E

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The arc length over the interval [π4,π2] for the given function.

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Chapter 8.2, Problem 30E

Chapter 8.2, Problem 32E

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Chapter 8 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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The arc length over the interval [ π 4 , π 2 ] for the given function.

Solution Summary: The author explains the formula of the integral of mathrmsecx.

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To compute:

The arc length over the interval [π4,π2] for the given function.

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Chapter 8 Solutions

The arc length over the interval [ π 4 , π 2 ] for the given function.

Solution Summary: The author explains the formula of the integral of mathrmsecx.

Concept explainers

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To compute: The arc length over the interval [π4,π2] for the given function.

Want to see the full answer?

Chapter 8 Solutions

To compute:

The arc length over the interval [π4,π2] for the given function.