So here is the problem:
Let's say we have some function $f(x,y)$
And we have some value $a$, where $a =\int_S f(x,y)dxdy$
From the set of surfaces $\{S\}$ where the above is true, find the minimal $S'$. I realise that this might possibly be non-unique, so here are some constraints: the surface $S$ is defined as:
$a =\int_S f(x,y)dxdy = \int_{0}^{g(x)}\int_{0}^{b}f(x,y)dxdy$
i.e a trapezoid where one of the sides is $g(x)$
So just find $g(x)$ which minimizes the surface $S'$ for which above is true (integral of f(x,y) evaluated over the surface S gives a)
