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: 26


$\int_{4}^{9} \int_{\sqrt y}^{3} f(x,y) \ dx \ dy = \int_{2}^{3} \int_{4}^{x^2} f(x,y) \ dy \ dx$

Work Step by Step

We are given the domain $0 \leq x \leq 4$ and $x \leq y \leq 4$. The iterated integral can be written for the domain $4 \leq y \leq x^2$ and $2 \leq x \leq 3$ as: $\iint_{D} f(x,y) d A= \int_{4}^{9} \int_{\sqrt y}^{3} f(x,y) \ dx \ dy = \int_{2}^{3} \int_{4}^{x^2} f(x,y) \ dy \ dx$
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