20. Let S be the closed region in the first quadrant of the xy-plane bounded by y = 6x², y = 0, x = 0, and x = 1. What is the volume of the solid obtained by revolving S about the line x = -1?

Rotating a vertical differential piece within the enclosed region of thickness dx about the line x = -1 creates a thin walled open cylinder with height y, whose differential volume, dV, is given by, 

Integrate the above equation over the interval [0,1] to obtain the total volume created by rotating the entire region. That is,