Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 442: 85


$2 \pi$

Work Step by Step

We calculate the volume as follows: Volume $=2 \int_0^{\infty} \pi (e^{-x/2})^2 \ dx\\=2\pi \int_0^{\infty} (e^{-x/2})^2 \ dx \\=2\pi \lim\limits_{R \to \infty}[-e^{-x}]_0^R\\=-2 \pi \lim\limits_{R \to \infty} (e^{-R}-1)\\=2 \pi (1-0)\\=2 \pi$
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.