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Math Help - Green's Theorem Proof Misunderstanding

  1. #1
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    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?
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  2. #2
    Super Member Rebesques's Avatar
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    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).
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