Calculus

Find the volume of the solid generated by revolving region bound by y=x^2, y=0, and x=2 about the x axis.

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  1. Volume = ∫ y^2 dx from 0 to 2
    = π∫ x^4 dx from 0 to 2

    easy to integrate, and evaluate.

    to check enter "π∫ x^4 dx from 0 to 2" into
    https://www.wolframalpha.com/

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    Reiny
  2. using discs of thickness dx,
    v = ∫[0,2] πr^2 dx = ∫[0,2] πx^4 dx = 32π/5
    using shells of thickness dy,
    v = ∫[0,4] 2πrh dy = ∫[0,4] 2πy(2-√y) dy = 32π/5

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    oobleck

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