Note from your transformation that and . Now, note that our region is a rectangle at 45° in the xy axes, and out bounding lines can be rewritten as: , , , and , so we have bounds in uv of , , and . Does that help?
Use the transformation:
x = (u+v)/2
y = (v−u)/2
double integral bounded by R of: (x − y)(x + y)dxdy
where R is the region bounded by the lines y = x + 2, y = x, y = −x + 2 and
y = −x + 4.
Again...its the bounds of the integral that are killing me. Thanks ahead of time my book is just terrible.