Posted by Elyse on .
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 
Steve,
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