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what is Greens Thm means to be

OCW Scholar - Multivariable Calculus
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Green's theorem establishes a relationship between the line integral of a vector field along a curve C and the double integral of that same vector field over the region R enclosed by C. This second integral is, more precisely, the double integral of the curl of the above-mentioned vector field over the region R. Green's theorem (along with the more general Stokes' theorem) is of great importance in Physics since it is the reason why any vector field whose curl is zero is (in general) conservative. Should there be any mistakes in the paragraph above I would appreciate it if you let me now.

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