1. The problem statement, all variables and given/known data Consider a free-electron gas at a temperature T such that kT << E_f Write down the expression for the electron number desnity N/V for electrons that have an energy in excess of of E_f. Show by making the change of variables (E-E_f)/kT = x. that the number desnity is proportional to T. Calculate an expression for N/V under these circumstances, making the use of that the fact that the ∫ from 0 to infinity of dx/(exp(x)+1) = ln 2 [Hint: In working out the integral over E the integrand is such that (x+E_f)^1/2 = E_f^(1/2) 2. Relevant equations I'm not sure where to start with this one. I know N is the Fermi Dirac distribution N(E) = 2/(exp( (E-E_f)/kT) + 1) but after that I'm not sure. 3. The attempt at a solution I'm a bit confused about what the question is asking. So I just looked up the equation for a Fermi Dirac distribution and tried to relate it to what I need. I'm not sure where the integral comes into play in this.