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Math Help - interval convergence

  1. #1
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    Jan 2010
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    interval convergence


    For the values of p at which the integral converges, evaluate it.

    I found the values of p in the interval to be from (-inf, 1), but I'm not sure how to calculate the integral itself. any help would be greatly appreciated!
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  2. #2
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    Jul 2009
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    For p < 1:
    \int_{0}^{1} \frac{1}{x^p} \: dx = \int_{0}^{1} x^{-p} \: dx = \left[ \frac{x^{-p+1}}{-p+1} \right]_{0}^{1} = \frac{1}{1-p}.
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