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calculus

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determine the volume of the solid of revolution generated by revolving the region bounded by y=x^3-x^5, y=0, x=0 and x=1 about the line x=3

  • calculus -

    check to be sure that the graph lies all on one side of the axis for the interval. It does.

    So, volume is

    v = ∫[0,1] pi (R^2-r^2) dx
    where R = 3, r = 3-y
    = pi∫[0,1] 9 - (3-(x^3-x^5))^2 dx
    = pi∫[0,1] -x^10 + 2x^8 - x^6 - 6x^5 + 6x^3 dx
    = pi(-1/11 x^11 + 2/9 x^9 - 1/7 x^7 - x^6 + 3/2 x^4) [0,1]
    = 677/1386

  • calculus -

    *pi

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