Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.3 - Trigonometric Integrals - Exercises 8.3 - Page 462: 31



Work Step by Step

We integrate as follows: \begin{align*} \int_{0}^{\pi / 2} \theta \sqrt{1-\cos 2 \theta} d \theta\\&=\int_{0}^{\pi / 2} \theta \sqrt{2}|\sin \theta| d \theta\\ &=\sqrt{2} \int_{0}^{\pi / 2} \theta \sin \theta d \theta\\ &=\sqrt{2}[-\theta \cos \theta+\sin \theta]\bigg|_{0}^{\pi / 2}\\ &=\sqrt{2} \end{align*}
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.