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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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How does Green's Theorem change from the original formula if we consider a clockwise line integral instead of counter-clockwise??
Original form \[\oint_\limits C \phi dx+\psi dy=\iint_\limits R(\frac{\partial \psi}{\partial x}-\frac{\partial \phi}{\partial x})dxdy\]

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Other answers:

you get a minus answer for the integral, ie a minus area!
\[-\iint_\limits R (\frac{\partial \psi}{\partial x}-\frac{\partial \phi}{\partial y})dxdy?\]
so \[\iint_\limits R (\frac{\partial \phi}{\partial y}-\frac{\partial \psi}{\partial x})dxdy\] If we go clockwise ?
yes, its all definitional if you go the other way you get a negative relationship between the area integral and the line integral. so we could all agree from now on that we'll go clockwise, but we could just swicth round Greens Theorem, and life would go on
Is it like switching the positive and negative charges and things would still work out(it's just a convention)
indeed

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