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: 50



Work Step by Step

\begin{align*} \int_{0}^{ \pi/2}\cos^3xdx&= \int_{0}^{ \pi/2}\cos^2x\cos xdx \\ &= \int_{0}^{ \pi/2}(1-\sin^2x)\cos xdx \\ &= \left(\sin x -\frac{1}{3}\sin ^3x\right) \bigg|_{0}^{\pi/2}\\ &=\frac{2}{3} \end{align*}
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