# Evaluate the following iterated integrals. ∫02∫014xy dx dy

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## Answered question

2021-02-25

Evaluate the following iterated integrals.

${\int}_{0}^{2}{\int}_{0}^{1}4xy\text{}dx\text{}dy$

### Answer & Explanation

$\text{Given integral}$

${\int}_{0}^{2}{\int}_{0}^{1}4xy\text{}dx\text{}dy$

$={\int}_{0}^{2}4[xdx]ydy$

$={\int}_{0}^{2}4\frac{{x}^{2}}{2}ydy$

$={\int}_{0}^{2}2[{x}^{2}{]}_{0}^{1}ydy$

$={\int}_{0}^{2}2[{1}^{2}-{0}^{2}]ydy$

$={\int}_{0}^{2}2ydy$

$=2[\frac{{y}^{2}}{2}{]}_{0}^{2}$

$=[{y}^{2}{]}_{0}^{2}$

$={2}^{2}-{0}^{2}$

$=4$

$\text{Therefore, the result of}{\int}_{0}^{2}{\int}_{0}^{1}4xy\text{}dx\text{}dy\text{}is\text{}4.$

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