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: 24


$\ln 2(e-1)$

Work Step by Step

The iterated integral can be calculated as: $\iint_{D} f(x,y) d A= \int_{1}^{e} \int_{0}^{y} (x+y)^{-1} \ dx \ dy \\= \int_{1}^{e} [\ln (x+y)]_0^y \ dy\\= \int_{1}^{e} (\ln 2y-\ln y) \ dy \\= \int_1^e \ln 2 \ dy \\=[y \ln 2][_1^e \\=e \ln 2 -\ln 2 \\=\ln 2(e-1)$
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