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Integral with stepfunction

  1. Mar 18, 2005 #1
    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

    [tex]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[/tex]

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

    [tex]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}[/tex]

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