Each shell has thickness dx, so
v = ∫[0,2] 2πrh dx
where r = 9-x and h = 8-y
v = ∫[0,2] 2π(9-x)(8-x^3) dx = 984π/5
as a check, using discs (washers) of thickness dy,
v = ∫[0,8] π(R^2-r^2) dy
where R=9 and r = 9-x
v = ∫[0,8] π(9^2-(9-∛y)^2) dy = 984π/5
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
y = x3, y = 8, x = 0; about x = 9
1 answer
1 answer