I have a question about an integral I have to solve. The question is: compute the following integral: $$\nu=\int \frac{dk}{(2 \pi)^3} \delta(\epsilon + E_F -E(k)) $$
express it in terms of $v_F$, $k_F$.
And given is also: We can approximate the energy by $E(k)-E_F=\hbar v_F (\delta k)$, $(\delta k) = |k|-k_F << k_F$.
So I evaluated this integral and got the answer $$ \frac{2}{(2 \pi)^3 |\hbar v_F|} $$
But this answer does not depend on $k_F$, so I am assuming that I did something wromg. I searched the whole internet for the answer, but couldn't find it..
Can somebody please help me?