Hello, it may look long but if written down- is really quite short, I have only included a detailed explanation to try and be more clear. My question is; I am doing a change of variable which doesn't seem to 'fit' the theory of finding the jacobian to make the transformation. It seems to me that I make a straightforward substitution: The integral is \int\int_A f'(t) ln( f(x) - f(t) + t - x)dxdt In my area, x <= t so the order cannot be switched. I make the following change of variable: Let r=x-f(x) and h(r) = x and let s=t-f(t) and h(s)=t notice that this gives f(x)=h(r)-r and f(t)=h(s)-s, hence f'(t)dxdt = dxf'(t)dt = h'(r)dr(h'(s) - 1)ds=h'(r)(h'(s)-1)drds. Now the integral appears to be \int\int_A' ln(r-s)h'(r)(h'(s)-1)drds Is this correct-can I do this change of variable without actually doing the jacobian. It seems that I do not actually have the integral \int\int f(x,y) dxdt in this case to make the transformation with the jacobian so I am wondering if there is anything wrong with the way I have done this?