The volume is given by the integral
[tex]\displaystyle2\pi\int_2^5x(x-1)\,\mathrm dx[/tex]
using the shell method. We approximate the solid of revolution with hollow cylinders with radius [tex]x-1[/tex] and height [tex]x[/tex].
[tex]\displaystyle2\pi\int_2^5x^2-x\,\mathrm dx=2\pi\left(\frac{x^3}3-\frac{x^2}2\right)\bigg|_{x=2}^{x=5}=57\pi[/tex]
