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Greens theorem boundary of a rectangle

  1. Aug 1, 2014 #1
    1. The problem statement, all variables and given/known data

    ##\mathscr{C}: x=1,x=3,y=2,y=3##

    ##\int_\mathscr{C} (xy^2-y^3)dx+(-5x^2+y^3)dy##

    2. Relevant equations



    3. The attempt at a solution

    ##\frac{\partial Q}{\partial x} = -10x^2 \,\,; \frac{\partial P}{\partial y} = 2xy-3y^2##

    ##\int\int_\mathscr{C} \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} dA = \displaystyle \int_{2}^{3}\int_{1}^{3} (-10x^2-2xy+3y^2)dxdy = -\frac{206}{3}##
     
  2. jcsd
  3. Aug 1, 2014 #2

    vela

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    You miscalculated dQ/dx.
     
  4. Aug 1, 2014 #3
    oh haha, -10x not ##-10x^2## thanks
     
  5. Aug 2, 2014 #4

    HallsofIvy

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    Of course, it is easy to do the integration around the path directly as a check. Have you done that?
     
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