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## Homework Statement

As a part of bigger HW problem, I need to calculate the integral:

[itex]\oint[/itex][[itex]\hat{r}[/itex]+[itex]\hat{z}[/itex]]d[itex]\phi[/itex]

## Homework Equations

## The Attempt at a Solution

In cylindrical coordinates:

=[[itex]\hat{r}[/itex]+[itex]\hat{z}[/itex]] [itex]\oint[/itex]d[itex]\phi[/itex]

=2∏[[itex]\hat{r}[/itex]+[itex]\hat{z}[/itex]]

On the other hand if I convert it to Cartesian coordinates:

[itex]\oint[/itex][cos[itex]\phi[/itex][itex]\hat{x}[/itex]+sin[itex]\phi[/itex][itex]\hat{y}[/itex]+ [itex]\hat{z}[/itex]]d[itex]\phi[/itex]

=2∏[itex]\hat{z}[/itex]

So, what is it that I am doing wrong in the case with cylindrical coordinates? I'm sure I'm missing something very basic.

Thanks.