integration/ boundary conditions

Hi guys,

I regard a particle in an Potential.

I have callculated the partition function and the probability density function [itex]F_{1}[/itex].

$$
H= \frac{p^{2}_{x}}{2m}
+ \frac{p^{2}_{z}}{2m}+ \frac{p^{2}_{\phi}}{2I}+ mgz
$$

For callculating an average value I do:
$$
<mgz>=\int \limits_{\color{Brown}?}^{\color{Brown}?}dx\int \limits_{\color{Brown}?}^{\color{blue}+ \color{blue}\infty}dz\int \limits_{\color{Brown}?}^{\color{Brown}?}d\phi~~~\int \limits_{-\infty}^{+\infty}dp_{x}\int \limits_{-\infty}^{+\infty}dp_{z}\int \limits_{-\infty}^{+\infty}dp_{\phi}
~
~~~~F_{1} ~mgz
$$

The boundary conditions are:
$$
0 \le x \le L \\
0 \le z \le {\color{blue} + \color{blue}\infty}\\
0\le \phi \le 2\pi \\
$$

Do I have to integrate to [itex]+/- \infty[/itex] or to the boundary conditions?

Thanks a lot
Abby
:approve: