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\[\int\limits_{?}^{?} (xy+x-y)dy + (xy+x+y)dx \]
Circle formula: \[x ^{2} + y ^{2} - ax = 0\]

Are you sure? I think you need to use polar coordinates.

Ok, I'll try it and see how it goes.

Here's my try to solve it using polar coordinates.

That's a*cos(theta)...Typo.

I should've mentioned it. I'm using Green's theorem.

since it is closed , consider green theorem

that's what we used, look at the scan above

(xy+x-y)dy + (xy+x+y)dx
N dy + M dx
Nx= y-1
My= x+1
\[\int \int Nx- My dx dy\]

Nx=y+1

\[\int \int (y-x ) dx dy\]

just integrate over circle

\[\int_0^{2\pi} \int_0^{ \frac{a}{2} cos(\theta)} a/2(sin(\theta))-(cos(\theta)) r dr d\theta\]