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\textbf{Multiple Integration}

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

Evaluate the following double integral by inspection.

$\int \! \int_T (x+y) \,dA$

where $T$ is the parallelogram with the points $(2,2),\ (1,-1),\
(-2,-2)$ and $(-1,1)$ as vertices.


\textbf{Answer}

$\begin{array}{l}
T \textrm{is symmetric about }x+y=0 \rm{\ so} \\
\int \! \int_T (x+y) \,dA =0
\end{array}
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