Yours Truly answers: We are used to exercise problems that ask us to set up integrals for a given region that is revolved about a given axis. So, we feel puzzled when we are asked a reverse question. Namely, given an integral, figure out what solid it represents. We would truly understand solids of revolution when we answer such questions.
 

Step 1.	Disk or Shell Method?
	An integral resulting from each method has a specific appearance. For example,
		is of the form  π·[f (x)]2dx, which indicates a disk method.
		would be of the form  2πx · f (x) dx, which indicates a shell method.
	So, our example uses a disk method.
Step 2.	Choice of a Variable
	Recall that the choice of a variable, x  or  y, indicates along which axis the thickness of a disk or a shell is measured. So, by looking at the tail end of the integral, the  dx  indicates that the thickness of the disk is measured along the x-axis. This analysis correctly positions the disk in 3D space.
Step 3.	Analyze f (x)
	In the disk method, f (x) is the radius of the disk. That is why we want to graph  y = f (x), which automatically gives us the region of revolution. So, let’s graph  y = 2x – x2.
Step 4.	Computation
	The actual computation of the integral is quite simple and left as an exercise. Expand the integrand and antidifferentiate it.