Stuck “easily showing that…” in Modinos

I’m currently stuck on Modinos’ derivation of the the number of electrons when cross a unit area per unit time, with total energy between E and E+dE and normal energy between W and W+dW .

N(E,W) dE dW = \frac{m}{2 \pi^2 \hbar^3} n(E) dE dW

where n(E) is the Fermi-Dirac distribution.   The blocking issue is integrating over an unusual region or k-vector 3 space where {E,W} under the triple integral indicates only states with total energy between E and E+dE and normal energy between W and W+dW corresponding to v_z>0 included in the integration.

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