Chapter 4.4, Problem 15P

For an ideal gas of $N$ molecules, the number of molecules with speeds $\le v$ is given by the formula $n(v)=\frac{4a^{3}N}{\sqrt{\pi }}{\displaystyle {\int }_0^v{x}^2}{e}^{-a^2{x}^2}dx$, where $a$ is a constant and $N$ is the total number of molecules. If $N={10}^{26},$ estimate the number of molecules with speeds between $v=1/a$ and $1.01/a$.