1. The problem statement, all variables and given/known data In thermal equilibrium, the particle in a gas are distributed in velocity space according to the Maxwell distribution f(v) = A*exp(-mv^2/(2KT)) What is the average velocity ? What is the most probable velocity ? 2. Relevant equations <v> = ∫∫∫vf(v)d3v = (0 to infinty) ∫∫∫vxf(v)d3vx^ + ∫∫∫vyf(v)d3vy^ + ∫∫∫vzf(v)d3vz^ 3. The attempt at a solution I started with the vy coordinate [0 to inf] ∫∫∫vyAexp(-mv^2/(2KT))dy = ∫[0 to 2pi]∫[0 to pi][0 to inf]vyA*exp(-mv2/(2KT))*v2y sin(θ)dθdvdφ = 4piA∫vy3exp(-mv^2/(2KT)) dv = Here is the problem, if i evaluate the integral i got a non-zero value. I know the 3 integrals should be zero since they are mult. of odd times even. And the most probable velocity is just the derivative of the f(v) function by resp. coordinate right ?