Answer
$\frac{3}{\pi}.$
Work Step by Step
The average is given by
$$
\frac{1}{\pi / 6-0} \int_{0}^{\pi / 6} \cos x d x=\frac{6}{\pi} \int_{0}^{\pi / 6} \cos x d x=\left.\frac{6}{\pi} \sin x\right|_{0} ^{\pi / 6}=\frac{3}{\pi}.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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