IF these are closed paths then you can convert to a surface integral over the region they bound, using Stoke's theorem. If they do not, you could "close" the paths in an infinite number of ways give different representations.
I have a region from inner radius to outer radius and from lower angle to upper angle (region is a piece of circular ring) - two edges are at constant radius and two are at constant angle. Do you have any equation for Stoke's theorem in polar coordinates.
I found equation on this page http://www.calpoly.edu/~dhartig/Page...olarCoords.pdf and I got what I wanted.