Infinite intervals of integration Evaluate the | Ch 7.7 - 19E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 19E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Problem 19E

Infinite intervals of integration Evaluate the following integrals or state that they diverge.

Step-by-Step Solution:

Problem 19E

Infinite intervals of integration
Evaluate the following integrals or state that they diverge.
$\int\limits_{2}^{\infty{}}\frac{x}{{\left({x+2}\right)}^{2}}dx$

Solution:
Step 1
For this integral, first we arrange the integral as follows.
$I=\int\limits_{\ }^{\ }\frac{x}{{\left({x+2}\right)}^{2}}dx$
$=\int\limits_{\ }^{\ }\frac{x+2-2}{{\left({x+2}\right)}^{2}}dx$
$=\int\limits_{\ }^{\ }\frac{x+2}{{\left({x+2}\right)}^{2}}dx-\frac{2}{{\left({x+2}\right)}^{2}}dx$
$=\int\limits_{\ }^{\ }\frac{1}{{\left({x+2}\right)}^{\ }}dx-\frac{2}{{\left({x+2}\right)}^{2}}dx$
$=ln\left({x+2}\right)+\frac{2}{{\left({x+2}\right)}^{\ }}+C$

Step 2 of 3

Chapter 7.7, Problem 19E is Solved

Step 3 of 3

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

The full step-by-step solution to problem: 19E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 19E from 7.7 chapter was answered, more than 368 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: diverge, evaluate, infinite, Integrals, Integration. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. The answer to “Infinite intervals of integration Evaluate the following integrals or state that they diverge.” is broken down into a number of easy to follow steps, and 13 words.