Calculus: Early Transcendentals 8th Edition

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

Chapter 5 - Section 5.5 - The Substitution Rule - 5.5 Exercises: 11

Answer

$$\int\cos(\pi t/2)dt=\frac{2}{\pi}\sin(\pi t/2)+C$$

Work Step by Step

$$A=\int\cos(\pi t/2)dt$$ Let $u=\frac{\pi t}{2}$ Then $du=\frac{\pi}{2}dt$. So $dt=\frac{2}{\pi}du$ Substitute into $A$, we have $$A=\int\cos u(\frac{2}{\pi})du$$ $$A=\frac{2}{\pi}\int\cos udu$$ $$A=\frac{2}{\pi}(\sin u)+C$$ $$A=\frac{2}{\pi}\sin(\pi t/2)+C$$
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