$$\lim_{R\to \infty}\int_{C}f(z)\ dz=\int_0^{\pi}f(Re^{i\theta})iRe^{i\theta}\ d\theta=0$$ $f(z)$ is an analytic function, $z=Re^{i\theta}$ & C is the semicircle in the upper half complex plane
I don't know how to proceed. Please help me prove this integral. thanks