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Math Help - Green's Theorem Integral

  1. #1
    Junior Member
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    Green's Theorem Integral

    Hi, I am having trouble with the following problem:



    Evaluate the integral for

    on the curve C consisting of the x-axis from x=0 to x=2, the parabola up to the y-axis, and the y-axis down to the origin.






    This is what I did so far:


    F(x,y)= <6xy^3,6x^2y^2>

     <br />
\int\int_{D} =[(6x^2y^2)*\frac{\partial}{\partial x}-(6xy^3)\frac{\partial}{\partial y}] dA <br />

     <br />
= \int_{0}^{2} \int_{4-x^2}^{0} [12xy^2-18xy^2] dy dx <br />

    = 64

    But, this is not right. Please help me out..

    Many thanks.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by althaemenes View Post
    Hi, I am having trouble with the following problem:



    Evaluate the integral for

    on the curve C consisting of the x-axis from x=0 to x=2, the parabola up to the y-axis, and the y-axis down to the origin.






    This is what I did so far:


    F(x,y)= <6xy^3,6x^2y^2>

     <br />
\int\int_{D} =[(6x^2y^2)*\frac{\partial}{\partial x}-(6xy^3)\frac{\partial}{\partial y}] dA <br />

     <br />
= \int_{0}^{2} \int_{4-x^2}^{0} [12xy^2-18xy^2] dy dx <br />

    = 64

    But, this is not right. Please help me out..

    Many thanks.
    Your limits of integration on y are reversed! XD

    It should be \int_{0}^{2} \int_{0}^{4-x^2} \left[12xy^2-18xy^2\right] \,dy \,dx
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