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 859: 45



Work Step by Step

The domain $D$ for given region can be expressed as: $-2 \leq x \leq 2$ and $0 \leq y \leq 4-x^2$ The iterated integral can be calculated as: $\iint_{D} f(x,y) d A=\int_{-2}^2 \int_{0}^{4-x^2} (40-10y) \ dy dx\\=\int_{-2}^2 (40y-5y^2)_0^{4-x^2} \ dx\\=\int_{-2}^2 [40(4-x^2)-5(4-x^2)^2] \ dx \\=\int_{-2}^2 [160-40x^2-80+40x^2-5x^4] \ dx \\=\int_{-2}^2 (80-5x^4) \ dx \\=[80 x-x^5]_{-2}^{2}\\=256$
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