TITLE: Physical intuition behind Green's theorem?
QUESTION [6 upvotes]: I get what the theorem is saying. The circulation of the curve is equal to adding up the "microscopic" curls. But why? Why does adding up the "microscopic curls" give you the circulation? Could someone give me an explanation of it using a physical analogy? I.e. an object rotating in moving body of water?

REPLY [6 votes]: The 'microscopic' curls cancel along all their shared boundaries, because they always go in opposite directions. The only thing you're left with is the curl along the 'macroscopic' exterior boundary.
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Added. See comment below.