# Evaluate the following iterated integrals. int_0^2int_0^1 4xy dx dy

Evaluate the following iterated integrals.
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d2saint0
$\text{Given integral}$

$={\int }_{0}^{2}4\left[xdx\right]ydy$
$={\int }_{0}^{2}4\frac{{x}^{2}}{2}ydy$
$={\int }_{0}^{2}2\left[{x}^{2}{\right]}_{0}^{1}ydy$
$={\int }_{0}^{2}2\left[{1}^{2}-{0}^{2}\right]ydy$
$={\int }_{0}^{2}2ydy$
$=2\left[\frac{{y}^{2}}{2}{\right]}_{0}^{2}$
$=\left[{y}^{2}{\right]}_{0}^{2}$
$={2}^{2}-{0}^{2}$
$=4$