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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.

$\int \! \int_{x^2+y^2\le1} (4x^2y^3-x+5) \,dA$


\textbf{Answer}

$\begin{array}{l}
\int \! \int_{x^2+y^2\le1} (4x^2y^3-x+5) \,dA\\
=0-0+5 (\textrm{area of disk}) \ \ (rm{by\ symmetry})\\
=-\pi\times4\times\frac{1}{2}(1)(1) = -2\pi
\end{array}
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\end{array}$

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