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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 $z=1-x^2$ and over the region $0 \le x \le 1$, $0 \le y \le x$.


\textbf{Answer}

\begin{eqnarray*}
V & = & \int_0^1 \,dx \int_0^x (1-x^2) \,dy\\
& = & \int_0^1 (1-x^2)x \,dx\\
& = & \frac{1}{2} - \frac{1}{4} = \frac{1}{4} \textrm{cu. units}
\end{eqnarray*}

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