You forgot about the Jacobian. It's the factor you have to multiply by when you do a change of variable in multiple integration. Like when you switch to polar coordinates and you have to multiply by r.
I am slightly confused on the following problem:
Change the order of integration of:
by making the substitution u = x, v = 2y-x.
Doing so I get:
However...it should apparently become:
That's where I am confused. I was able to see how to change the limits of integration, but I don't know where this 1/2 comes from. Consequently my answer is twice as much as it should be. Thanks for any help.