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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 - ,

    P = y^2
    Q = xy

    ç[0,9]ç[0(ãx)](ÝQ/Ýx-Ýp/Ýy)dy dx

    ç[0, 9]ç[0, ãx ](y-2y)dy dx

    ç[0,9]ç[0, ãx](-y)dy dx

    ç[0,9]-x/2 dx

    =(-x^2)/4 [0, 9] = (-81)/4

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