Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis

Answer 1

The curves intersect at (0,0) and (2,2)

v = ∫[0,2] π(R^2-r^2) dy
where R = √y and r = y/2
v = ∫[0,2] π(y-y^2/4) dy
= π(y^2/2 - y^3/12) [0,2]
= 4π/3