# Thread: How to compute this double integral?

1. ## How to compute this double integral?

How to compute this double integral?$I=\displaystyle\int\displaystyle\int_{R( xy)}(3x+6y)^2dA$. How to find out R(xy) here? In the original problem $R(xy)$ region is given where A,B,C,D are labels for sides.

$A=x+2y=2,B=x-2y=2,C=x+2y=-2,D=x-2y=-2$

How this region is calculated?here R(xy) is the region shown in the plot below. (A,B,C, and D are labels for the 4 sides.)

2. ## Re: How to compute this double integral?

$\large \displaystyle \int_{-2}^0 \int_{-\left(1+\frac x 2\right)}^{1+\frac x 2}~(3x+6y)^2~dy~dx + \int_0^2 \int_{\frac x 2 - 1}^{1-\frac x 2}~(3x+6y)^2~dy~dx$