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Math Help - Greens Theorem (Need Help)

  1. #1
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    Greens Theorem (Need Help)

    Can someone show me step by step how to work this problem out please.

    Let C be the triangle with vertices (0,0), (1,0), and (1,2). Find the following line integral by two methods, directly and using greens theorem.

    2xy^2dx + yx^2dy

    Thanks!!!
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  2. #2
    Eater of Worlds
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    Per Green's Theorem:

    The equation of the line from (0,0) to (1,2) is y=2x.

    f(x,y)=2xy^{2}, \;\ g(x,y)=x^{2}y

    \int_{C}2xy^{2}dx+x^{2}ydy=\int\int\left[\frac{\partial}{\partial{x}}(x^{2}y)-\frac{\partial}{\partial{y}}(2xy^{2})\right]dA=\int_{0}^{1}\int_{0}^{2x}(-2xy)dydx

    Can you finish up?.
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  3. #3
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    im lost.

    When you start the problem you have to find P and Q right?

    So I think that is P = 2xy^2 Q = yx^2
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  4. #4
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    so than dQ/ dx = ? dp/dy = ?

    From what you were showing me how does this relate to that
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