University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.8 - Antiderivatives - Exercises - Page 271: 14


a) $\sin \pi x+C$ b) $\sin \dfrac{\pi x}{2}+C$ c) $\dfrac{2}{\pi} \sin \dfrac{\pi x}{2}+\pi \sin x+C$

Work Step by Step

a) The anti-derivative is: $\pi (\dfrac{1}{\pi} \sin \pi x)+C=\sin \pi x+C$ b) The anti-derivative is: $\dfrac{\pi}{2}\dfrac{1}{\pi/2} \sin \dfrac{\pi x}{2}+C=\sin \dfrac{\pi x}{2}+C$ c) The anti-derivative is: $\dfrac{1}{\pi/2} \sin \dfrac{\pi x}{2}+\pi \sin x+C=\dfrac{2}{\pi} \sin \dfrac{\pi x}{2}+\pi \sin x+C$
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