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March 27, 2017

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Use Green's theorem to evaluate the integral:
y^(2)dx+xy dy
where C is the boundary of the region lying between the graphs of y=0,
y=sqrt(x), and x=9

  • Calculus - ,

    Using the definition, we have
    P = y^2
    Q = xy

    and the integral becomes

    ∫[0,9]∫[0,√x] (∂Q/∂x - ∂P/∂y) dy dx
    = ∫[0,9]∫[0,√x] (y - 2y) dy dx
    = ∫[0,9]∫[0,√x] -y dy dx
    = ∫[0,9] -x/2 dx
    = -x^2/4 [0,9]
    = -81/4

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