Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 13 - Multiple Integration - 13.1 Double Integrals over Rectangular Regions - 13.1 Exercises: 5

Answer

$\int_{0}^{2} \int_{0}^{1} 4xy$ $dxdy = 4$

Work Step by Step

$\int_{0}^{2} \int_{0}^{1} 4xy$ $dxdy$ Integrate with respect to $x$: $\int_{0}^{2} 2x^2y |_0^1$ $dy$ $=$ $\int_{0}^{2} [2(1^2)y - 2(0)^2y]$ $dy$ $=$ $\int_{0}^{2}2y$ $dy$ Integrate with respect to $y$: $y^2|_{0}^{2} = 2^2-0^2=4$
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