Disks

Find the volume of the solid obtained by rotating about the x-axis the area under the curve f(x)=sqrt(5x) from x=0 to x=1.

> restart;

> f:=sqrt(5*x);

The region to be rotated is

> L:=[[1,0],[1,f(1)]]:

> plot({L,f},x=0..1);

The graph of the volume is

> with(plots);

> tubeplot([x,0,0],x=0..1,radius=f(x),axes=normal);

The volume is given by

> Int(Pi*f^2,x=0..1);

> value(%);