$\iint 1/(x+y)$ in region bounded by $x=0, y=0, x+y =1, x+y = 4$ using following transformation: $T(u,v) = (u - uv, uv)$. I want to make sure that my method is correct
Calculating the jacobian, I get $u$ since $x+y = u$, i get that $1 < u < 4$ Additionally, $v = y/y+x$ and thus at $x = 0$, we have $v = 0$ and at $y = 0$ we have $v = 1$.
So this the double integral is equivalent to $\iint(1/u)u dudv$ over the area $[1,4]$x$[0,1]$ which is easily solved
I am not sure about the method I employed, any help would be greatly appreciated.