Proof of Green’s Theorem

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A proof of Green's Theorem: a theorem that relates the line integral around a curve to a double integral over the region inside.
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Thank you for this demonstration, immensely useful. Others are a bit cursory and 'hand-wavey' but knowing the mechanics of these theorems is indispensable.

charleswoodard
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Nicely done! Not too rigorous but the idea was there... Thank you!

emanoelsouza
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Is there any no C such that R is not a union of type 1 and type 2 regions?

Gurralious