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Math Help - For b>0, deduce that f(x)=x^3 is integrable on [0,b]

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    For b>0, deduce that f(x)=x^3 is integrable on [0,b]

    This question is a peculiar one, to say the least.

    For b>0, let P be the partition of [0,b] into n equal subintervals. Calculate both S_P and s_P for f(x)=x^3 and prove that
    J(=glb(S_P))\leq 1/4b^4(1+1/n)^2 and that I(=lub(s_P))\geq 1/4b^4(1-1/n)^2
    for any positive n.
    Deduce that f(x) is integrable on [0,b] and \int_0^b x^3dx=1/4b^4.
    NOTE: \sum_{k=1}^n k^3=1/4n^2(n+1)^2

    EDIT: I found some help on the question, though his answer is a little long. I'll post a link below to his work.
    http://answers.yahoo.com/question/in...8081532AALd5im

    If he made any mistakes, be sure to point them out.
    Last edited by Runty; November 18th 2010 at 09:39 AM. Reason: Got the question answered; link provided
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