Integrating Equation 37.5 over all energies gives the total number of states per unit volume in a

Question:

Integrating Equation 37.5 over all energies gives the total number of states per unit volume in a metal. Therefore, integrating from E = 0 to E = E_F?that is, over the occupied states only gives the number of conduction electrons per unit volume. Carry out this integration to show that the electron number density is given by