Chapter 13 - Multiple Integration - 13.1 Double Integrals over Rectangular Regions - 13.1 Exercises - Page 970: 5

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

$\int_{0}^{2} \int_{0}^{1} 4xy$ $dxdy$ 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 $y$: $y^2|_{0}^{2} = 2^2-0^2=4$