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: 52



Work Step by Step

\begin{align*} \int_{0}^{ \pi/2}\sin^2x\cos^3 xdx&= \int_{0}^{ \pi/2}\sin^2x\cos^2 x\cos xdx \\ &= \int_{0}^{ \pi/2}\sin^2x (1-\sin^2x) \cos xdx \\ &=\int_{0}^{ \pi/2} (\sin^2x-\sin^4x) \cos xdx \\ &= \left( \frac{1}{3}\sin^3x -\frac{1}{5}\sin^5x \right) \bigg|_{0}^{\pi/2}\\ &=\frac{2}{15} \end{align*}
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