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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Find the exact length of the curve.

15. y = ln(sec x), 0 ≤ xπ/4

To determine

The exact length of the curve.

Explanation

Given information:

The curve function is y=ln(secx) (1)

The limits are a=0 and b=π4.

Calculation:

The expression to find the length of the curve (L) is shown below:

L=ab1+(dydx)2dx (2)

Here, the derivative of the function y is dydx, the lower limit is a, and the upper limit is b.

Differentiate Equation (1) with respect to x.

dydx=secxtanxsecx=tanx

Substitute tanx for dydx, 0 for a, and π4 for b in Equation (2)

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