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\begin{center}
\textbf{Multiple Integration}

\textit{\textbf{Double Integrals}}
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\textbf{Question}

Evaluate the following double integral by inspection.

$\int \! \int_{x^2+y^2\le a^2} \sqrt{a^2-x^2-y^2} \,dA$


\textbf{Answer}

$\begin{array}{l}
\int \! \int_{x^2+y^2\le a^2} \sqrt{a^2-x^2-y^2} \,dA\\
=\textrm{volume of hemisphere}\\
=\frac{1}{2} \left ( \frac{4}{3} \pi a^3 \right ) = \frac{2}{3}\pi a^3
\end{array}
 \ \ \
\begin{array}{c}
\epsfig{file=MI-1A-7.eps, width=40mm}
\end{array}$


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