Solution :
[tex]$y=x^{3/2}, \ \ y =8, \ \ x=0$[/tex]
[tex]$v=2 \pi \int_0^4 x (8-x^{3/2}) \ dx$[/tex]
[tex]$= 2\pi \left(\frac{8x^2}{2}-\frac{x^{7/2}}{7/2}\ \left|_0^4[/tex]
[tex]$=2\pi \left( 4x^2-\frac{2}{7}x^{7/2}\ |_0^4$[/tex]
[tex]$=2\pi \left( 64-\frac{2}{7} \times 32 \times 4 \right)$[/tex]
[tex]$=2\pi \left(1-\frac{4}{7} \right) 64$[/tex]
[tex]$=128 \pi \times \frac{3}{7}$[/tex]
[tex]$=\frac{384 \pi}{7}$[/tex]
