# Complex Analysis: countour integral

1. Jan 7, 2012

### Bonjournoo

1. The problem statement, all variables and given/known data

Compute the contour integral I around the following curve $\Gamma$:

$I = \int_\Gamma \dfraq{dz}{z^2 +1}$

see picture:
http://dl.dropbox.com/u/26643017/Screen%20Shot%202012-01-07%20at%2010.39.58.png [Broken]

2. Relevant equations

3. The attempt at a solution

$\Gamma$ is an open curve, but even if you close it with a line from A to B an the real axis, you may not use cauchy's theorem and calculate it with the residue theorem, because it is not a "smooth curve"...

Last edited by a moderator: May 5, 2017
2. Jan 7, 2012

### Dick

The curve doesn't have to be "smooth" to apply Cauchy's theorem. It only has to be rectifiable. Piecewise smooth is plenty good enough.