Use Green's theorem to evaluate the integral:

Question

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

Answer 1

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