Double integral and Green's theorem

rashida564 · Jan 6, 2020

Hi everyone, I was wondering if it was possible to calculate a double integral by converting it to a line integral, using the greens theorem, and if so is it possible to get a non zero answer. if we were working on a rectangular region

jedishrfu · Jan 6, 2020

You have to be sure the double integral meets the Green's Theorem criteria:

https://en.wikipedia.org/wiki/Green's_theoremLet C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then

$(L\,dx+M\,dy)=\iint _{D}\left({\frac {\partial M}{\partial x}}-{\frac {\partial L}{\partial y}}\right)\,dx\,dy$

c
where the path of integration along C is anticlockwise.[2][3]

NOTE: had problem getting C under the line integral.

Double integral and Green's theorem

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Double integral and Green's theorem

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