Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Section 15.2 - Double Integrals over General Regions - Exercises 15.2 - Page 882: 16


a) $\int_{0}^1 \int_{0}^{1} f(x,y) dy dx$ (b) $\int_{0}^{1} \int_{0}^{e^y} f(x,y) dx dy$

Work Step by Step

(a) For vertical cross-sections, the region $R$ can be defined as: $\iint_{R} dA=\iint_{R_1} dA+\iint_{R_1} dA$ $= \int_{0}^1 \int_{0}^{1} f(x,y) dy dx +\int_{1}^{e} \int_{\ln x}^{1} f(x,y) dy dx $ (b) For horizontal cross-sections, the region $R$ can be defined as: $\iint_{R} dA= \int_{0}^{1} \int_{0}^{e^y} f(x,y) dx dy$
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