Hello, it may look long but if written down-(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Double integral/change of variable

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