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Math Help - Use Green's formula

  1. #1
    Junior Member
    Joined
    Dec 2009
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    33

    Use Green's formula

    Let P(x,y),Q(x,y)\in C^1(R^2) and

    \oint\limits_{L(M_0,R)}^{}P(x,y)dx+Q(x,y)dy=0, where

    L(M_0,R):y=y_0+\sqrt{R^2-(x-x_0)^2} (uper semicircle)

    where  M_0(x_0,y_0)\in {\Bbb R}^2 and R\in {\Bbb R}^+ are arbitrary.

    Prove that

    P(x,y)\equiv 0 and \frac{\partial {Q(x,y)}}{\partial x}\equiv 0

    Hint: Prove first that P(x,y)\equiv 0 , by use parametric integrals. What must we do to apply Green's formula?
    Last edited by ns1954; January 30th 2010 at 01:10 PM.
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