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 858: 7



Work Step by Step

The domain $D$ for given region can be expressed as: $0 \leq y \leq 2$ and $y\leq x\leq 4$ The iterated integral can be calculated as: $\iint_{D} x^2y d A=\int_0^2 \int_{y}^4 x^2y dx dy\\=\int_0^2 \dfrac{x^3y}{3}|_{y}^{4} dy \\=\int_0^2 \dfrac{y^3}{3}(64-y^3) \ dy \\=[\dfrac{32y^2}{3}-\dfrac{y^5}{15}]_0^2 \\=40.5$
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