Calculus (3rd Edition)

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

Chapter 8 - Techniques of Integration - 8.2 Trigonometric Integrals - Exercises - Page 403: 49



Work Step by Step

\begin{align*} \int_{0}^{2\pi}\sin^2 xdx&= \frac{1}{2} \int_{0}^{2\pi} \left( 1-\cos 2x\right) dx \\ &= \frac{1}{2}\left(x -\frac{1}{2}\sin 2x\right) \bigg|_{0}^{2\pi}\\ &=\pi \end{align*}
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