I'm trying to solve this line integral:
$$\oint_{L} |x|dxdy$$ $$L: x^2 + y^2 = 1$$ So by dividing the domain into 2 half (left and right) and using Green's Theorem I can solve it.
My question is when dividing a closed domain like this, will it become 2 opened or closed domain? And is there any better way to solve this problem? Thank you in advance!