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: 8

Answer

$3e^{12}+e^8$

Work Step by Step

The domain $D$ for the given region can be expressed as: $4 \leq y \leq 8$ and $4\leq x\leq 12-x$ The iterated integral can be calculated as: $\iint_{D} e^{x+y} d A=\int_4^8 \int_{4}^{12-x} e^{x+y} dx dy\\=\int_4^8 e^x (e^{12-x}-e^4) \ dx\\=\int_4^8 (e^{12}-e^{4+x}) \ dx \\=4e^{12} e^{12}+e^8\\=3e^{12}+e^8\approx 491245.3$
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