In this problem we use the change of variables $x=2 s + t$, $y = s - t$ to compute the integral $\int_R (x+y)\,dA$, where $R$ is the parallelogram with vertices $(x,y)=(0,0)$, $(4,2)$, $(7,-1)$, and $(3,-3)$.

First find the magnitude of the Jacobian, $\left|\frac{\partial(x,y)}{\partial(s,t)}\right| =$ .

Then, with $a =$ , $b =$ ,
$c =$ , and $d =$ ,
$\int_R (x+y)\,dA = \int_a^b\,\int_c^d\, ($ $s +$ $t +$ $)\; dt\, ds$ =