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!