Chapter 18.5, Problem 18.5TYU

A quantity of gas containing N molecules has a speed distribution function f(v). How many molecules have speeds between v₁ and v₂ > v₁? (i) ${\displaystyle {\int }_0^{v_2}f(v)dv}-{\displaystyle {\int }_0^{v_1}f(v)dv}$; (ii) $N[{\displaystyle {\int }_0^{v_2}f(v)dv}-{\displaystyle {\int }_0^{v_1}f(v)dv}]$; (iii) ${\displaystyle {\int }_0^{v_1}f(v)dv}-{\displaystyle {\int }_0^{v_2}f(v)dv}$; (iv) $N[{\displaystyle {\int }_0^{v_1}f(v)dv}-{\displaystyle {\int }_0^{v_2}f(v)dv}]$; (v) none of these.