where

(4.124)

v and erf(x) is the error function defined as

(4.125)

The values of erf(x) as a function of x are given in Table 4.2

Table 4.2 Values of Error Functions

To compute the number of molecules having velocities lying between 0 and v_mp the value of x will lie between 0 and 1. Then, from Eq.(4.123),

(4.126)

Hence,  41.67% of the molecules have speeds between 0 and v_mp. Similarly, to the number of molecules having x - components of velocity
between 0 and v_x.

(4.127)