using shells of thickness dy,
v = ∫[3,11] 2πrh dy
where r = y-3 and h = 16-(y-7)^2
v = ∫[3,11] 2π(y-3)(16-(y-7)^2) dy = 2048π/3
using discs (washers) of thickness dx,
v = ∫[0,16] π(R^2-r^2) dx
where r = 7-√x-3 and R = 7+√x-3
v = ∫[0,16] π((4+√x)^2-(4-√x)^2) dx = 2048π/3
The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.
x = (y − 7)^2, x = 16; about y = 3
1 answer