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Math Help - Line Integrals - is this allowed?!!

  1. #1
    Member billym's Avatar
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    Line Integrals - is this allowed?!!

    Let R be a region bounded by the curves:

    y^2-x-1=0 and y^2+x-1=0

    I want to verify Green's Theorem in the plane for:

    \oint_{\partial{R}}(y^2+x)\, dx +(xy+1)\, dy

    ***

    For the line integrals part, since the two curves intersect at (-1,0) and (1,0).

    Can I use:

    \int_{0}^{0}(y^2+x)\, \frac{dx}{dy} \, dy + (xy+1) \, dy

    In which case they will both be equal to zero and I won't have to integrating?
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  2. #2
    Super Member
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     \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}


     = y - 2y = -y


    Although it is not zero , i still like to congratulate you because it is an odd

    function


    In fact , it is equal to  - ( ~y-coordinate~of~the~center~of~mass~) \times (~area~)
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