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\begin{center}
\textbf{Multiple Integration}

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

\textbf{Question}

Evaluate the following double integral by inspection.

$\int \! \int_{S} (x+y) \,dA$,

where $S$ is the square $0 \le x \le a$, $0 \le y \le a$.


\textbf{Answer}

From the symmetry of $S$, with respect to $x$ and $y$
$$ \ $$
$\begin{array}{l}
\int \! \int_{S} (x+y) \,dA\\
=2\times\textrm{ volume of wedge}\\
=2 \times \frac{1}{2}(a^2)a=a^3
\end{array}
 \ \ \
\begin{array}{c}
\epsfig{file=MI-1A-9.eps, width=40mm}
\end{array}$

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