Chapter 8.1, Problem 8E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### 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=âˆ’1 and b=1.

Calculation:

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

L=âˆ«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=ey2Ã—2y=2yey<

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started