About maxwell-boltzmann distribution

[asdff529]

Base on maxwell-boltzmann distribution,we can calculate the average velocity of gas molecule .
i read a book and it proves like that
average velocity=$\int vf(v) dv$
I don't understand why we don't have to divide it by N because we should be calculating the average,but not the total.
Would anyone tell me where i went wrong

 

[dauto]

f(v) is a probability distribution, not the total number so you have already divided by N when calculating the probability distribution.

 

[glsalierno]

by multiplying each bin of the velocities, you already normalize the velocity distribution