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: 17


$ \dfrac{1754}{15}$

Work Step by Step

The iterated integral can be calculated as: $\iint_{D} f(x,y) d A= \int_{1}^{3} \int_{x}^{2x+1} x^2y \ dy \ dx \\= \int_{1}^{3} [\dfrac{x^2y^2}{2}]_x^{2x+1} \ dy\\=(\dfrac{1}{2}) \int_{1}^{3} [x^2(4x^2+4x+1)-x^2(x^2)] \ dx\\=(\dfrac{1}{2})[\dfrac{3x^5}{5}+x^4+\dfrac{x^3}{3}]_1^3 \\= \dfrac{1754}{15}$
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