Compute $\int \limits_{C} F.dr$ for $F(x,y)=(x-y,x+y)$ and $C$ is the curve given by $x^2+y^2=x+y$ while going clockwise.
So this is a circle which is $$(x-\frac12)^2+(y-\frac12)^2=(\frac1{\sqrt2})^2$$
To parameterise it, I was thinking we can let $ x = \frac12 + \frac1{\sqrt2}\cos(\theta) $ and $y = \frac12 + \frac1{\sqrt2}\sin(\theta) $ so we can have $r(\theta)=(\ \frac12 + \frac1{\sqrt2}\cos(\theta), \frac12 + \frac1{\sqrt2}\sin(\theta) $ but what are the limits?