Calculus- Finding Volume By Cylindrical Shells

Sometimes using the methods of washers or discs creates an unpleasant integral.
This is why the method of Cylindrical Shells is used.

To help visualize this method, think of a solid can in the shape of a cylinder.

Now imagine unraveling the paper label that covers the outer surface of the can. Although it is small, it is still a portion of the total volume.

If we keep unraveling this can in thin strips such as the paper label, and we then sum all of the strips up we will have the total volume.  A visual representation of this is shown in figure 1. 

if you unravel each strip and flatten in out, it would have a height, length (same as circumference), and width (represented as 'dx').

In figure 2 the equation for finding the volume using Cylindrical Shells is shown.

Question (Figure 3): Find the volume of the region bounded by y=  x²  , x= -2 and x = 2
The radius is along the x-axis of length 'x'
The height extends from the x-axis up to the curve.   
The thickness of each sheet is represented by 'dx'
Input all of these parameters into the equation.

Post any questions in the comments.
Double-click on image to make it bigger.