1. The problem statement, all variables and given/known data Given the integral integral(0,infinity)(v^3*e^(-a*v^2)dv)=a^-2/2 Calculate the average speed v(average) of molecules in a gas using the Maxwell-Boltzmann distribution function. 2. Relevant equations v^2(average)=integral(0,infinity)(v^2*v(t)dv) 3. The attempt at a solution I took the general approach. integral(0,infinity)(f(v)dv)=(4/pi)*(m/(2*k*T))^(3/2)*integral(0,infinity)(v^2*e^(-mv^2/(2*k*t))dv) However, I could not find out how to make a substitution for a in order to get the v^3 into the equation.