Equipartition Thm: mv_x^2/2 = k_B T/2

[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

 

[Chandra Prayaga]

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