In the exercise you will use the change of variables $u = 4x + 2y$, $v = 3x + 3y$ to find
$\iint_R (4x + 2y)e^{12x^2 + 18xy + 6y^2} dA$
where R is the region bounded by $4x + 2y = -2$, $4x + 2y = 0$, $3x + 3y = 3$ and $3x + 3y = 1$
$\iint_R (4x + 2y)e^{12x^2 + 18xy + 6y^2} dA = \int_A^B \int_C^D F(u, v) dv du$
where $A = -2$, $B = \text{ }$, $C = \text{ }$, $D = 1$, $F(u, v) = \text{ }$
After the change of variables this integral is simple if done the right way. In particular we obtain
$\iint_R (4x + 2y)e^{12x^2 + 18xy + 6y^2} dA = $
