Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question

y = 27x³,    y = 0,    x = 1;    about x = 2

Answer 1

CYLINDRICAL SHELLS

∫₀¹ 2π [ 2− x ] 27 x³ d x

DISC METHOD

∫₀²⁷ π { [ 2−( y^1/3 ) /3 ]² −1² } d y