Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - 7.1 Integration by Parts - 7.1 Exercises - Page 516: 6


$-\frac{1}{\pi}(x-1) cos \pi x + \frac{1}{\pi^2} sin \pi x +C$

Work Step by Step

Let $u = x-1, dv = sin \pi x dx$ and $du = dx, v = -\frac{1}{\pi} cos \pi x$ then $\int (x-1) sin \pi x dx$ $= -\frac{1}{\pi}(x-1) cos \pi x - \int -\frac{1}{\pi} cos \pi x dx$ $= -\frac{1}{\pi} (x-1) cos \pi x + \frac{1}{\pi} \int cos \pi x dx$ $=-\frac{1}{\pi}(x-1) cos \pi x + \frac{1}{\pi^2} sin \pi x +C$
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