How do I evaluate this complex integral?

Question

I've been given a integral to solve: For $r>2 \ $ let $ \ C_r = \{r e^{it}: 0 \le t \le \pi\ \} \ $ show that

$$ \lim_{r \to \infty} \int_{C_r} \frac{1}{(z^2 + 4)^2}dz = 0 $$ Could someone give my a hint on where to start?

Answer 1

Parametrize the path as $z=re^{it}$ then use squeeze theorem to show that the magnitude of the integral goes to $0$.