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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...Asked by Elyse
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
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
Answers
Answered by
kuai
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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