Consider an integral of the form:
$$\int f(u,v) dt$$
where $t=\dfrac{u+v}{2}$: how do I change variables in such a way to get an integral in $du$ and $dv$ instead of $dt$?
This kind of integral came out in my work on general relativity: $t$ is coordinate time and $u$ and $v$ are retarded and advanced null coordinates.