Find the volume generated by revolving the plane area within

Question

y=2x^2 , y=0 , x=0 , x=5; about x axis

Answer 1

using discs of thickness dx,
v = ∫[0,5] πr^2 dx
where r=y
v = ∫[0,5] π(2x^2)^2 dx

using shells of thickness dy,
v = ∫[0,50] 2πrh dy
where r=y and h = 5-x
v = ∫[0,50] 2πy(5-√(y/2)) dy