Simple integral in cylindrical coordinates

[Vagrant]

Homework Statement

As a part of bigger HW problem, I need to calculate the integral:
\oint[\hat{r}+\hat{z}]d\phi

Homework Equations

The Attempt at a Solution

In cylindrical coordinates:
=[\hat{r}+\hat{z}] \ointd\phi
=2∏[\hat{r}+\hat{z}]

On the other hand if I convert it to Cartesian coordinates:
\oint[cos\phi\hat{x}+sin\phi\hat{y}+ \hat{z}]d\phi
=2∏\hat{z}

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.

 

[SammyS]

Homework Statement

As a part of bigger HW problem, I need to calculate the integral:
\oint[\hat{r}+\hat{z}]d\phi

Homework Equations

The Attempt at a Solution

In cylindrical coordinates:
=[\hat{r}+\hat{z}] \ointd\phi
=2∏[\hat{r}+\hat{z}]

On the other hand if I convert it to Cartesian coordinates:
\oint[cos\phi\hat{x}+sin\phi\hat{y}+ \hat{z}]d\phi
=2∏\hat{z}

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.

\hat{r} is a function of \phi\ .

 

[Vagrant]

Sorry, but could you please explain this a bit?
I can visualize that \hat{r} is a function of \phi(unit circle on x-y plane centered at origin) for cartesian coordinates, but I'm drawing a blank when it comes to cylindrical coordinates.