University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 356: 38



Work Step by Step

We need to integrate the integral to compute the volume. We have: Area $=\pi r^2=\pi (1-\tan^2 y)$ $$Volume = \pi \times \int_{0}^{\pi/4} (1- \tan^2 (y) ) \space dy \\= \pi (y-(\tan y -y)]_{0}^{\pi/4 } \\= \pi [2y-\tan (y) ]_{0}^{\pi/4} \\=\pi(\dfrac{\pi}{2}-1)$$
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.