The region bounded by y = x^2 and y = 4 is rotated about the line y = -1. The volume of the solid generated is given by

Answer 1

using discs,

v = ∫[0,2] π(R^2-r^2) dx
where R=4 and r =y=x^2

using shells,

v = ∫[0,4] 2πrh dy
where r=y and h=x=√y