Chapter 8.8, Problem 35E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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 2 1 x − 1 3   d x

To determine
Whether the improper integral 021x13dx converges or diverges.

Explanation

Consider the provided integral,

âˆ«021xâˆ’13dx=âˆ«011xâˆ’13dx+âˆ«121xâˆ’13dx=limbâ†’1âˆ’âˆ«0b1xâˆ’13dx+limaâ†’1+âˆ«a21xâˆ’13dx

Now, use the formula:

âˆ«abf(x)dx=limcâ†’a+âˆ«cbf(x)dxâˆ«abf(x)dx=limcâ†’bâˆ’âˆ«acf(x)dx

Then,

âˆ«021xâˆ’13dx=limbâ†’1âˆ’âˆ«0b1xâˆ’13dx+limaâ†’1+âˆ«a21xâˆ’13dx=limbâ†’1âˆ’âˆ«0b(xâˆ’1)âˆ’1/3dx+limaâ†’1+âˆ«a2(xâˆ’1)âˆ’1/3dx

Let xâˆ’1=u. Then, dx=du

### 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