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Homework Help: Maths (calculus) problem

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data
    The distribution of the speed v of molecules, mass m, in a gas in thermal equilibrium at temperature T is given by:


    where k is the boltzmann constant and A is the normalising constant. Determine A such that

    [tex]\int[/tex] between 0 and [tex]\infty[/tex] P(v)dv=1

    2. Relevant equations

    3. The attempt at a solution
    Obviously the main problem is I don't think it's very easy to directly integrate this equation and so I assume there is some trick for why between those values you can see a value for A where that last relationship will hold. Just a point in the right direction would be helpful, thanks.
  2. jcsd
  3. Nov 2, 2009 #2


    Staff: Mentor

    Here's your integral, nicely formatted in LaTeX:
    [tex]\int_0^{\infty} Av^2e^{-\frac{0.5mv^2}{kT}}dv[/tex]

    I don't think there is any trick -- integration by parts will probably do the job. I would split it up as u = v, dw = ve-(0.5mv2/kT)dw.
  4. Nov 2, 2009 #3
    To make it simpler I'll say that m/kT is B.

    But when you integrate ve^-Bv^2 the first time you get (-e^-Bv^2)/2B

    But then for integration by parts you need to integrate this again which as far as I can see you can't do using the basic integration techniques I know.
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