Green's theorem is a vector identity which is equivalent to the Curl Theorem in the Plane. Over a region in the
plane with boundary ,
If the region is on the left when traveling around , then Area of can be computed using
See also Curl Theorem, Divergence Theorem
References
Arfken, G. ``Gauss's Theorem.'' §1.11 in
Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985.