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: 38



Work Step by Step

The domain $D$ for given region can be expressed as: $x \leq y \leq x+1$ and $0 \leq x \leq 1$ The iterated integral can be calculated as: $\iint_{D} f(x,y) d A=\int_0^1 \int_{x}^{x+1} e^{x} dy dx\\=\int_0^1 (ye^x)_x^{x+1} dy \\=\int_0^1 [(x+1)e^x-xe^x] \ dx \\=\int_0^1 e^x \ dx \\=[e^x]_0^1 \\=e-1$
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