Use the function y = 2x to find the function values.
These are all nice points above the x-axis, so they are effectively radii of circles, once the curve is rotated around the x-axis.
So, now you can find the area of these three circles since you know the radii!
Area circle 1 = πr2 = π x (21)2 = 4π
Area circle 2 = πr2 = π x (21.5)2 = 8π
Area circle 3 = πr2 = π x (22)2 = 16π
Rather than use Simpson's Rule to find the area, use it to find the volume.
Volume = h/3 x (A1 + 4A2 + A3)
= 0.5/3 x (4π + 4 x 8π + 16n)
= 0.5/3 x 52π
= 27.2 cubic units