Residue Method for Integrating Complex Functions

[player1_1_1]

Homework Statement

$$\int\limits^{\infty}_{-\infty}\frac{\mbox{d}x}{x^2+1}$$
and i must count this using residues

The Attempt at a Solution

$$I=2\pi i\left(\mbox{res}_i\frac{1}{z^2+1}\right)=2\pi i\left(\lim_{z\to i}(z-i)\frac{1}{(z-i)(z+i)}\right)=2\pi i\left(-\frac12i}\right)=\pi$$
correct?

 

[player1_1_1]

i don't know why edit doesn't work, but now i came to that these points must be for $$\Im(z)\ge0$$ and result will be $$\pi$$ now, is this solution correct now?
there should have been $$\Im(z)\ge0$$

 

[micromass]

Yes, the answer $$\pi$$ is correct. And it seems that your method is also good!