Then, imagine the area being approximated using horizontal rectangular strips.
Each rectangular strip has length and width , (some small change in y).
When you rotate the strips, they create cylinders, each of radius and depth .
So the volume of each strip is , and therefore the volume of the region is approximated by
As you increase the number of subdivisions, i.e. make and , this sum converges to an integral, and the approximation becomes exact.
So , where are your y endpoints.