Finding the Normalizing Constant for the Maxwell-Boltzmann Distribution

[henryc09]

Homework Statement

The distribution of the speed v of molecules, mass m, in a gas in thermal equilibrium at temperature T is given by:

P(v)dv=Av²e^{-(0.5mv^2)/(kT)}dv

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

$$\int$$ between 0 and $$\infty$$ P(v)dv=1

Homework Equations

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.

 

[Mark44]

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

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.

 

[henryc09]

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.