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\textbf{Multiple Integration}

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

Find the volume of the given solid

Below $z=1/(x+y)$ and over the region in the $xy$-plane bounded by
$x=1$, $x=2$, $y=0$ and $y=x$.


\textbf{Answer}

\begin{eqnarray*}
V & = & \int_1^2 \,dx \int_0^x \frac{1}{x+y} \,dy\\
& = & \int_1^2 \,dx \left ( \left. \ln (x+y) \right |_{y=0}^{y=x}
\right )\\
& = & \int_1^2 (\ln 2x - \ln x) \,dx\\
& = & \ln 2 \int_1^2 \,dx = \ln 2 \textrm{cu. units}
\end{eqnarray*}

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