# Equipartition theorem

1. Mar 25, 2013

### michael892

show that
$$< \frac{mv_{x}^{2}}{2}> \equiv s\int_{-\infty }^{\infty} \frac{mv_{x}^{2}}{2} \rho (v_{x}) dv_{x}=\frac{k_{B}T}{2}$$

im stuck

Last edited: Mar 26, 2013
2. Mar 29, 2013

### Chandra Prayaga

Plug in the expression for ρ(vx) inside the integral and then actually calculate the integral, or look it up in a table of integrals.