Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 7 - Section 7.1 - Integration by Parts - 7.1 Exercises - Page 476: 29



Work Step by Step

$$\int_{0}^{\pi}x\,sin\,xcos\,x\,dx=\frac{1}{2}\int_{0}^{\pi}x\,sin\,2x\,dx$$ $$\frac{1}{2}\left[\left[-\frac{x\,cos\,2x}{2}\right]_{0}^{\pi}+\frac{1}{2}\int_{0}^{\pi}cos\,2x\,dx\right]$$ $$=-\frac{\pi}{4}+\frac{1}{4}\left[\frac{sin\,2x}{2}\right]_{0}^{\pi}$$ $$=-\frac{\pi}{4}$$
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