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March 27, 2017

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=1/x^4, y=0, x=2, x=9;
about y=–5

  • calculus - ,

    method: find the volume of the whole solid, then subtract the volume of the cylinder.

    Volume of whole solid
    = pi(integral)(1/x^4 + 5)^2 dx from 2 to 9
    = pi[-1/(7x^4) - 10/(3x^3 + 25x] from 2 to 9
    which came out to 551.077

    the volume of the cylinder is
    pi(5^2)(7) = 549.779

    so the volume of the shape you described is 1.298

    not too sure about my arithmetic.

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