(adsbygoogle = window.adsbygoogle || []).push({}); Questions about Green's Theorem

When asked to demonstrate that Green's Theorem works, I keep coming up with disagreeing answers. I've been able to do the double integrals for the area of a region over a function F just fine, but whenever I try to integrate the same function over the closed curve using the normal vector, I keep getting zero... Say, I was integrating a function over a square. The double integral over the area works out just fine, but when I break the curve up into 4 sides, and try integrating each of those, I keep getting zero, because the opposite sides of the square cancel each other out. I don't really know what I'm missing, and it's been driving me nuts.:grumpy: Is there anything obvious that I'm just missing somehow?

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# Problems with Greens' Theorem

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