   Chapter 8.8, Problem 101E

Chapter
Section
Textbook Problem

Finding a Value For what value of c does the integral ∫ 0 ∞ ( 1 x 2 + 1 − 1 x + 1 ) d x converge? Evaluate the integral for this value of c.

To determine

To calculate: The value of integral 0(1x2+1cx+1)dx and for what value of c it converges.

Explanation

Given:

The improper integral:

0(1x2+1cx+1)dx

Formula used:

To check for convergence, the following limit must exist.

abf(x)dx=limbabf(x)dx

The integral: 1x2+a2dx=ln|x+x2+a2|.

Calculation:

The integral can be solved as below:

0(1x2+1cx+1)dx=limb0b(1x2+1cx+1)dx=limb[ln|x+x2+1|cln|x+1|</

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