# Math Help - Green's Theorem Proof Misunderstanding

1. ## Green's Theorem Proof Misunderstanding

By the way, I also posted this in the Urgent Help section.

Okay, I get the half that is normally explained in the books which is the same as on wikipedia (http://en.wikipedia.org/wiki/Green's_theorem).

This is the best that I can explain this:

I understand the part of the explaination where integral of (P dx) = - double integral of (partial derivative of P with respect to y) dA.

I don't, however, understand why on the other half, integral of (Q dy) = double integral of (partial derivative of Q with respect to x) dA, does not have a negative sign in front of one of the two halves.

If essetially you are doing the same process twice, once with a type I region and the other time with a type II region, why does one half of the proof end up with a negative (which I understand) but not the other half?

2. Depends on the orientation of the curve, i.e which point is the initial one. Here the minus is needed to travel along the boundary in the positive direction (anti-clockwise).