A glass vase has the shape of the solid obtained by rotating

A glass vase has the shape of the solid obtained by rotating about the y-axis the area in the first quadrant lying between the curves y = (x^2) +1, y = 2(x^2) - 2 and the two axis; Determine how much glass (in units^3) is contained in the vase.

Solution

x^2+1=2*x^2-2 x^2=3/2 pi*integral from 0 to 3/2 of (x^2+1)^2-(2*x^2-2)^2 =351*pi/160=6.89 units^3