What I did:
u = x+y
so
x = u-y
y = u-x
x \geq 0
y \geq 0
y \leq 1-x
u-y \geq 0 \rightarrow u \geq y
u-x \geq 0 \rightarrow u \geq x
u <= 1
x \in [0,1]
y \in [0,1]
So
u \in [0,1]
And I don't know what to do about the integral and the Jacobian, etc :(
what to you think about?
Ps: OMG, tex...