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: 25


$\int_{0}^{4} \int_{x}^{4} f(x,y) \ dy \ dx = \int_{0}^{4} \int_{0}^{y} f(x,y) \ dx \ dy$

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 $0 \leq y \leq 4$ and $0 \leq x \leq y$ as: $\iint_{D} f(x,y) d A= \int_{0}^{4} \int_{x}^{4} f(x,y) \ dy \ dx = \int_{0}^{4} \int_{0}^{y} f(x,y) \ dx \ dy$
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