Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the line x=9.
y=x^2 ,y=0, x=3, x=6
using shells of thickness dx
v = ∫[3,6] 2πrh dx
where r = 9-x and h = y = x^2
v = ∫[3,6] 2π(9-x)x^2 dx = 1053π/2
check, using discs (washers) of thickness dy, you have to change boundaries at (3,9) so
v = π(6^2-3^2)*9 + ∫[9,36] π(R^2-r^2) dy
where R = 9-x = 9-√y and r = 3
∫[9,36] π((9-√y)^2-3^2) dy = 567π/2
so v = 243π + 567π/2 = 1053π/2