The given curve is rotated about the y-axis. Find the area of the resulting surface.
y = 4 − x2, 0 ≤ x ≤ 2
using shells of thickness dx,
v = ∫[0,2] 2πrh dx
where r = x and h = y = 4-x^2
v = ∫[0,2] 2πx(4-x^2) dx = 8π
using discs of thickness dy,
v = ∫[0,4] πr^2 dy
where r = x = √(4-y)
v = ∫[0,4] π(4-y) dy = 8π