Question Number 90055 by awlia last updated on 21/Apr/20
Commented by jagoll last updated on 21/Apr/20
$$\mathrm{vol}\:=\:\pi\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:\mathrm{dx}\: \\ $$$$=\:\pi\:\left\{\:−\frac{\mathrm{x}^{\mathrm{2}} \left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}\left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{4}} }{\mathrm{6}}−\frac{\left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{5}} }{\mathrm{60}}\:\right\}_{\mathrm{0}} ^{\mathrm{4}} \\ $$$$=\:\frac{\mathrm{4}×\mathrm{256}\pi}{\mathrm{60}}\:=\:\frac{\mathrm{256}\pi}{\mathrm{15}} \\ $$