Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - Chapter Review Exercises - Page 278: 59


$-\frac{3\sqrt 3}{2\pi} .$

Work Step by Step

We have \begin{align*} \int_{0}^{1} \cos \left(\frac{\pi}{3}(t+2)\right) d t&=\frac{3}{\pi}\int_{0}^{1} \frac{\pi}{3}\cos \left(\frac{\pi}{3}(t+2)\right) d t\\ &=\frac{3}{\pi} \sin\left(\frac{\pi}{3}(t+2)\right)|_{0}^{1}\\ &=\frac{3}{\pi} \left( \sin\left(\pi\right) - \sin \frac{2\pi}{3}\right)\\ &= -\frac{3\sqrt 3}{2\pi} . \end{align*}
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