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Math Help - Prove x^2 is integrable

  1. #1
    Super Member Anonymous1's Avatar
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    Prove x^2 is integrable

    Here is the question I'm working on:

    Prove directly from the definition of integrability that x^2 is integrable on any [a,b] \subset [0,\infty).

    I have just begun integrability, and am not so familiar with using the definition. I've set up the preliminaries, but do not know how to proceed. Any advice?

    ~Thanks.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Anonymous1 View Post
    Here is the question I'm working on:

    Prove directly from the definition of integrability that x^2 is integrable on any [a,b] \subset [0,\infty).

    I have just begun integrability, and am not so familiar with using the definition. I've set up the preliminaries, but do not know how to proceed. Any advice?

    ~Thanks.
    You are talking about this from a Riemann-Stieltjes integrable persepctive, correct?
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  3. #3
    Super Member Anonymous1's Avatar
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    Yes I was, but I actually found a solution, i.e., proving integrability for some arbitrary, but small mesh. The meat of it was cracked via MVT, and using mass cancelation of the resulting telescoping series.
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