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: 31


$e -2$

Work Step by Step

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