Question

Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?

Answer 1

I meant to phrase the question as, "What integral represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?"

Answer 2

using shells of thickness dx,

v = ∫[1,2] 2π(2-x)(x^3-1) dx

using discs of thickness dy,

v = ∫[1,8] π(2-∛y)^2 dy