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Let R be the region bounded by y=−3(x−1)(x−3) and the x-axis. Let S be the solid obtained by rotating R about the y-axis. The volume of S is given by Nπ. What is the value of N?

  • Calculus - ,

    v = ∫[1,3] 2πrh dx
    where r = x and h = y = −3(x−1)(x−3) so
    v = ∫[1,3] 2πx(−3(x−1)(x−3)) dx
    = -6π ∫[1,3] x^3 - 4x^2 + 3x dx
    = 16π

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