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\begin{center}
\textbf{Multiple Integration}

\textit{\textbf{Iteration of Double Integrals}}
\end{center}

\textbf{Question}


Calculate the given double integral by iteration.

$\ds \int\!\!\!\int_R x^2y^2 \,dA$

With $R$ being the same rectangle of part (a).


\textbf{Answer}

\begin{eqnarray*}
\int\!\!\!\int_R x^2y^2 \,dA & = & \int_0^a x^2 \,dx \int_0^b y^2
\,dy\\
& = & \frac{a^3}{3} \frac{b^3}{3} = \frac{a^3b^3}{9}
\end{eqnarray*}


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