(1) Compute the line integral $\int_c -y \,dx + x \,dy$, where C is a circle of radius r about the origin, travelled in a counterclockwise direction.
What happens if you travel around C clockwise?
(2) Compute the line integral
$\int_c \frac{-y \,dx + x \,dy}{x^2 + y^2}$
where C is a circle of radius r about the origin, travelled in a counterclockwise direction.
What happens if you travel around C clockwise?