In this lesson, we learned about Green's Theorem and how it can be used to compute line integrals along closed curves. By computing the double integral of the curl of a vector field over the region enclosed by the curve, we can avoid calculating the line integral directly. If the curl is zero, then the vector field is conservative, and we can use Green's Theorem to verify this property. However, if the vector field is not defined everywhere, then we cannot apply Green's Theorem, and the vector field may not be conservative, even if its curl is zero everywhere it is defined.
Learn about Green's Theorem and how it is used.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.