Chapter 2, Problem 97CP

Verify the normalization equation ${\displaystyle {\int }_0^{\infty }}f\left(v\right)dv=1$

In doing the integral, first make substitution $u=\sqrt{\frac{m}{2k_{B}T}}v=\frac{v}{v_p}.$ This "scaling" transformation gives you all features of the answer except for the integral, which is a dimensionless numerical factor. You'll need the formula ${\displaystyle {\int }_0^{\infty }{x}^2{e}^{-x^2}dx=\frac{\sqrt{\pi }}{4}}$ to find the numerical factor and verify the normalization.`