Problem

三、計算題（占 18 分）

16. (10 分) Compute the integral $\oint \dfrac{x-y}{x^2+y^2}\,\mathrm{d}x+\dfrac{x}{x^2+y^2}\,\mathrm{d}y$.

(a) (5 分) Over any closed curve $C$ not enclosing the origin.

(b) (5 分) Over the circle of radius $a$ centered at $(0,0)$.