The area enclosed by the loop of the curve 𝑦

2 = 𝑥(1 − 𝑥)2is revolved about the y-axis. Find the volume generated.

1 answer

using shells of thickness dx, and the symmetry of the region,
v = 2∫[0,1] 2πrh dx
where r = x and h = y
v = 2∫[0,1] 2πx*(1-x)√x dx = 16π/35