# Homework Help: Integral with stepfunction

1. Mar 18, 2005

### Pietjuh

For my statistical physics class I need to evaluate the following type of integral by iteration and I am not sure I'm doing it correctly

$$I_N = \int_0^{\infty}dx_1 \int_0^{\infty}dx_2\cdots \int_0^{\infty} \theta(a - \sum_{i=0}^N x_i) dx_N$$

Since i must iterate this integral I'm going to try and calculate the last integral. I then wrote
$$a' = a - \sum_{i=0}^{N-1} x_i$$
so,

$$I_N = \int_0^{\infty}dx_1 \int_0^{\infty}dx_2\cdots \int_0^{\infty} \theta(a' - x_N) dx_N = \int_0^{\infty}dx_1 \int_0^{\infty}dx_2\cdots \int_0^{a'} 1 dx_N = \int_0^{\infty}dx_1 \int_0^{\infty}dx_2\cdots \int_0^{\infty} a' dx_{N-1}$$

But this integral diverges!! Can someone tell me what I did wrong here?