# Homework Help: Maths (calculus) problem

1. Nov 2, 2009

### henryc09

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:

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

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. Nov 2, 2009

### Staff: Mentor

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.

3. Nov 2, 2009

### 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.