Find the volume of the solid generate by revolving about the y-axis and the area bounded by y=4-x^2 and y=0?

Answer 1

using shells of thickness dx,
v = ∫ 2πrh dx
where r = x and h = y
∫[0,2] 2πx(4-x^2) dx

since the y-axis is the axis of symmetry of the solid, the volume is generated twice, but I hope that doesn't matter