Calculus (3rd Edition)

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

Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 298: 41



Work Step by Step

The average is given by $$ \frac{1}{\pi / 6-0} \int_{0}^{\pi / 6} \cos x d x=\frac{6}{\pi} \int_{0}^{\pi / 6} \cos x d x=\left.\frac{6}{\pi} \sin x\right|_{0} ^{\pi / 6}=\frac{3}{\pi}. $$
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