# Line integral around a circle in polar coordinates

1. May 28, 2013

### JacobNielsen

I know that $\oint_{C}\mathrm{d}\vec{l} = 0$, for any closed curve C.
But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero.

Here is my approach : $\oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi = 2\pi\hat{\phi} \neq 0$
Since the line element [itex]\mathrm{d}\vec{l}[itex] is pointing in the azimuthal direction.

Where do I make a mistake?