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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

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

8. y2 = ln x, −1 ≤ y ≤ 1

To determine

To represent: An integral as the length of the curve.

The length of the curve.

Explanation

Given information:

The curve function is y2=lnx (1)

The limits are a=1 and b=1.

Calculation:

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

L=ab1+(dxdy)2dy (2)

Here, the derivative of the function x is dxdy, the lower limit is a, and the upper limit is b.

Rearrange Equation (1) as shown below.

x=ey2 (3)

Differentiate Equation (3) with respect to y.

dxdy=ey2×2y=2yey<

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