# How to evaluate int 2x-3y dA using change of variables

by AeroFunk
Tags: jacobians
 P: 40 Let R be the region bounded by the graphs of x+y=1, x+y=2, 2x-3y=2, and 2x-3y+5. Use the change of variables: $$x=1/5(3u+v)$$ $$y=1/5(2u-v)$$ to evaluate the integral: $$\iint(2x-3y)\,dA$$ I found the jachobian to be -1/5 and the limits of integration to be 1<=u<=2 2<=v<=5 so i set up the integral like this: $$\frac{-1}{5}\int_{2}^{5}\int_{2}^{1} vdv$$ and I get -21/5 which doesn't seem right(a negitive number??),what am I doing wrong?