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

  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?"

  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

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