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Math Help - Integal 1/x^p

  1. #1
    s3a
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    Integal 1/x^p

    Can someone explain to me how to do the following problem please?:

    "Find the values of p for which the integral converges and evaluate the integral for those values of p."

    Integral of 1/x^p dx on the interval [0,1]

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
    MHF Contributor

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    Taking the anti-derivative of \frac{1}{x^p}= x^{-p} would be a great place to start!
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  3. #3
    s3a
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    Yes,

    I found:
    when p = 1:
    ln|t| = infnity

    and

    when p ≠ 1:
    1/(1-p) * x^(1-p)

    but the book says:

    p < 1, 1/(1-p) and I don't quite understand what this means, it looks similar but different to what I did.
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