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Deriving the rms speed from the Maxwell speed distribution

  1. Nov 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Find vrms from the Maxwell speed distribution.

    Basically what I need to solve is the integral [itex]a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v [/itex]

    Where ##a## and ##x## are constants.

    2. Relevant equations

    $$a\int_0^∞ \! v^4e^{xv^2} \, \mathrm{d}v $$

    Where ##a## and ##x## are constants.

    3. The attempt at a solution

    I've tried u-substitution, subbing in u for ##v^2## and for ##v^{2.5}## but they end up not working.
     
    Last edited: Nov 20, 2013
  2. jcsd
  3. Nov 20, 2013 #2
    Nevermind, figured it out (integrate by parts a couple times).
     
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