Answer
$\frac{1}{\pi}.$
Work Step by Step
The average is given by
$$
\frac{1}{2-1} \int_{1}^{2} \frac{\sin (\pi / x)}{x^{2}} d x=\frac{1}{\pi} \int_{\pi / 2}^{\pi} \sin u d u=-\left.\frac{1}{\pi} \cos u\right|_{\pi / 2} ^{\pi}=\frac{1}{\pi}.
$$
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: 44
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