   Chapter 8.8, Problem 38E

Chapter
Section
Textbook Problem

Evaluating an Improper Integral In Exercises 33–48, determine whether the improper integral diverges or converges. Evaluate the integral if it converges, and check your results with the results obtained by using the integration capabilities of a graphing utility. ∫ 0 e ln   x 2   d x

To determine
Whether the improper integral 0elnx2dx converges or diverges.

Explanation

Consider the provided integral,

0elnx2dx=0e2lnxdx=20elnxdx

Now, use the formula:

abf(x)dx=limcbacf(x)dx

Then,

20elnxdx=2lima0+aelnxdx

Now, apply the formula of integration by parts:

udv=uvvdu

Then,

2lima0+aelnxdx=2lima0+[lnx(dx)∫</

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

Differentiate. y=x2tanx

Single Variable Calculus: Early Transcendentals, Volume I

Evaluate the indefinite integral. (lnx)2xdx

Single Variable Calculus: Early Transcendentals

Perform the indicated operation for the following. 1,205491

Contemporary Mathematics for Business & Consumers 