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: 19


$ \dfrac{e-2}{2}$

Work Step by Step

The domain $D$ for given region can be expressed as: $0 \leq x \leq 1$ and $1\leq y\leq e^{x^2}$ The iterated integral can be calculated as: $\iint_{D} f(x,y) d A= \int_{0}^{1} \int_{1}^{e^{x^2}} x \ dy \ dx \\= \int_{0}^{1} [xy]_1^{e^{x^2}} \ dx\\= \int_{0}^{1} [xe^{x^2}-x) \ dx \\=[\dfrac{e^{x^2}}{2}-\dfrac{x^2}{2}]_0^1 \\= \dfrac{e-2}{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.