Chapter 7.8, Problem 52E

### 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

# Use the Comparison Theorem to determine whether the integral is convergent or divergent.52. ∫ 0 ∞ arctan x 2 + e x   d x

To determine

To find: whether the integralfunction is convergent or divergent using Comparison Theorem.

Explanation

Given information:

The integral function is âˆ«0âˆžarctanx2+exâ€‰dx.

Calculation:

Show the integral function as follows:

âˆ«0âˆžarctanx2+exâ€‰dx (1)

Considerf and g are continuous function with f(x)â‰¥g(x)â‰¥0 for xâ‰¥a.

Part (a):

If âˆ«aâˆžf(x)dx is convergent, then âˆ«aâˆžg(x)dx is convergent.

Part (b):

If âˆ«aâˆžg(x)dx is divergent, then âˆ«aâˆžf(x)dx is divergent.

Consider the value of the function g(x)=arctanx2+ex (2)

Consider the value of the function f(x)=2ex (3)

Calculate the value of g(x) within limits [0,âˆž] using Equation (2).

Substitute 0 for x in Equation (2).

g(x)=arctanx2+ex=arctan(0)2+e0=0

Substitute âˆž for x in Equation (2).

g(x)=arctanx2+ex=arctan(âˆž)2+eâˆž=arctan(âˆž)âˆž=0

Calculate the value of f(x) within limits [0,âˆž] using Equation (3).

Substitute 0 for x in Equation (3).

f(x)=2ex=2e0=2

Substitute âˆž for x in Equation (3).

f(x)=2ex=2eâˆž=0

Compare the value of f(x) and g(x) within limits [0,âˆž]

### 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