
help with greens theorem
just trying figure this example out using greens theorem:
mapped counterclockwise, is the circle
enter as a multiple of pi
so using substitution,
so
and
so i got this far how does this end bit work?? do i integrate? where do i go from here...

Doesn't r vary from 0 to 9?.

oops yeah my mistake, so how would i proceed, from here, i know im supposed to change polars, but i dont know exactly how to solve this

Just integrate. You should know how to do this simple integration since you're in Calc III.
Now, integrate wrt to theta:
Now, multiply by 27:

any help with this?
help...(Doh)
int {[xy4x^4yysqrt(x^2+y^2+1/2y^2sinx]dx
+ [4xy^4+8/3x^3y^2+sqrtx^2+y^2ycosx]dy}
where r is the path mapped counterclockwise: along y=o,
0<x<1; then along x^2+y^2=1, from (1,0)to (1/sqrt2,1/sqrt2);
finally y=x from (1/sqrt2,1sqrt2) to (0,0)