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

**References**

Arfken, G. ``Gauss's Theorem.'' §1.11 in
*Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 57-61, 1985.

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1999-05-25