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Math Help - Integration by Parts & Volumes of Revolution

  1. #1
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    Integration by Parts & Volumes of Revolution

    For the integration sign I'll use a capital s.

    1) Find the volume of revolution when the area between y=(1/x), x=1, x=5, and y=0 is rotated about the x-axis.

    V= ((pie) S(1-5) (1/x)^2 dx)
    =(pie)(S(1-5))(1/x^2) dx
    =(pie)[1/(-3x^3)|(1-5)
    =(pie)[(1/((-3)(5)^3) - (1/((-3)(1)^3)]
    = -(1126(pie)) / 3

    Seems like a wrong answer so if anyone can help thank you.


    2) Find the average value of the function of f(x) = (x)^3 + (2)^2 - 5x over [-1,5].

    Not sure how to start this one
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  2. #2
    Junior Member
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    Oh shoot...my antiderivative is wrong. should be:

    1/-x right?

    So I got final answer of:

    4(pie) / 5
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