Applications to Green's Theorem in Economics?

I was wondering about possible of application of integration to economics (other than welfare), more specifically, how might Green's theorem be useful for an economist?

Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C . If G and H are functions of (x,y) defined on an open region containing D and have continuous partial derivatives there, then

$$\oint_C{(G\ dx + H\ dy) = \int\!\!\!\int_D {\left({{\partial H} \over {\partial x}} - {{\partial G} \over {\partial y}}\right)\ dx\ dy} }$$

where the path integral is traversed counterclockwise.

The idea behind this theorem is that if you have a line integral in two dimensions, then Green's theorem can be used to compute the integral: Green's theorem transforms the line integral around a simple closed curve $$C$$ into a double integral over the plane region $$D$$ bounded by $$C$$.