I’m having a little trouble understanding why Green’s Theorem is defined as;(adsbygoogle = window.adsbygoogle || []).push({});

∮_C P dx+Q dy = ∬_D [(δQ/δx)-(δP/δy)] dA

Instead of;

∮_C P dx+Q dy = ∬_D [(δQ/δx)+(δP/δy)] dA

When proving the theorem, in the first step you simply reverse the bounds of the second integral to get the result;

∮_C P dx = -∫_(x=a)^(x=b) ∫_(y=g_1 (x))^(y=g_2 (x)) δP/δy dydx

But in the second step, the bounds are kept how they are to keep the double integral positive. So you have;

∮_C Q dy = ∫_(y=a)^(y=b) ∫_(x=h_2 (y))^(x=h_1 (y)) δP/δy dxdy

So can anyone explain why the bounds were reversed in the step?

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# Green's Theorem?

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