Maxwell - Boltzmann Distribution Integral: Proving Its Normalization

[mopar969]

Show that the Maxwell - Boltzmann distribution integral: the integral of f(v) dv from zero to infinity is equal to one.

I know what the formula is but I am unsure on how to approach this problem. Please help in any way. Thanks.

Also, I know that the integral is the area under the curve of a function so the are must be 1 but how do I show this algebraically?

 

[cepheid]

You have to actually compute the integral. You have to integrate the function f(v) from 0 to ∞. The answer you get should be 1.

 

[mopar969]

Is there an easy way to integrate it because it is not an easy function?

 

[cepheid]

I found this page that might be of assistance:

http://quantummechanics.ucsd.edu/ph130a/130_notes/node87.html

First it tells you how to integrate a function of the form exp(-av²), where a is some constant. Then, the last two lines at the bottom show you how to use that result to determine the integral of a function of the form v²exp(-av²).

 

[mopar969]

Okay thanks for the site. I solved the integral and got 4pi((m/(2pikt))^(3/2))[(2kt)/(4m)][square root of((2pikt)/(m))]. But now how do I show that this equals one? Please help.