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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.

$\int \! \int_{R} \sqrt{b^2-y^2} \,dA$,

where $R$ is the rectangle $0 \le x \le a$, $o \le y \le b$.


\textbf{Answer}

$\begin{array}{l}
\int \! \int_{R} \sqrt{b^2-y^2} \,dA\\
=\textrm{volume of quarter cylinder}\\
=\frac{1}{4}(\pi b^2)a=\frac{1}{4} \pi ab^2
\end{array}
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\epsfig{file=MI-1A-11.eps, width=40mm}
\end{array}$

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