Calculus (3rd Edition)

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

Chapter 16 - Multiple Integration - 16.2 Double Integrals over More General Regions - Exercises - Page 860: 53


$\dfrac{2 }{3 \pi}$

Work Step by Step

The average height can be computed as: $\overline{h}=\dfrac{1}{Area \ of \ a \ Domain (D)} \iint_{D} f(x,y) d A\\=\dfrac{1}{\pi }\int_0^1 \int_{0}^{\pi} y^2 \sin x \ dx \ dy\\=\dfrac{1}{\pi }\int_0^1 (-y^2 \cos x )_0^{\pi} \ dy\\=[\dfrac{2y^3}{3 \pi}]_0^1 \\=\dfrac{2 }{3 \pi}$
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