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?
2 answers

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?"

using shells of thickness dx,
v = ∫[1,2] 2π(2x)(x^31) dx
using discs of thickness dy,
v = ∫[1,8] π(2∛y)^2 dy