Volumes by Integration: Disk Method
Now sketch a differential element, a volume disk, with thickness dx.
OK. Let’s write the equation for the volume of the disk, dV:
Now we have to get the whole equation in terms of x. Note that the radius of the disk, r = y. And y = 2x1/2. Let’s plug this into the equation for dV.
dV=p(2x1/2)2dx = p4xdx
Now we can integrate. This time, we’ll include limits. Note that the disk would sweep along the x axis from 0 to 4.