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\textbf{Multiple Integration}

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

Evaluate the following double integral by inspection.

$\int \! \int_{T} (1-x-y) \,dA$,

where $T$ it the triangle with vertices $(0,0), \ (1,0)$ and $(0,1)$.


\textbf{Answer}

$\begin{array}{l}
\int \! \int_{T} (1-x-y) \,dA\\
=\textrm{volume of tetrahedron}\\
=\frac{1}{3}\left ( \frac{1}{2}(1)(1) \right ) (1) = \frac{1}{6}
\end{array}
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