so i have the double integral (x-3y)da, and R is a triangular region with vertices (0,0) (1,2) (2,1). transformations are x=2u+v and y=u+2v
So i drew out the triangle and found equations for the 3 lines.
then i plugged in my transformations for each of these three equations.
the first equation left me with v=0
The second left me with u=0
the third with u=1-v
So i drew out this new triangle shape.
I want to make sure my bounds are correct, if i'm integrating wrong, i can figure that out.
so integrating with respect to u first, my bounds should be
then plug in the transformations for x-3y, and integrate away.
i came out with an answer of -6. but it's supposed to be -3. again, if i integrated wrong, i can figure that out. i've done it a few times and am still not getting -3, so i'm wondering if my bounds are wrong.