University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 8 - Section 8.7 - Improper Integrals - Exercises - Page 471: 10



Work Step by Step

Consider $f(x)= \int_{-\infty}^{2} \dfrac{2}{x^2+4} dx$ Since, we have $\lim\limits_{a \to -\infty} f(x)= \lim\limits_{a \to -\infty}\int_{a}^{2} \dfrac{2}{4[(x/2)^2+1]} dx=\lim\limits_{a \to -\infty}\int_{a}^{-2}[\tan^{-1} (1) -\tan^{-1} (a/2)] $ or, $=\lim\limits_{a \to -\infty} \dfrac{\pi}{4} - \tan^{-1} (a/2)$ or, $=\dfrac{\pi}{4} - (-\dfrac{\pi}{2})$ or, $=\dfrac{3\pi}{4}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.