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Math Help - integration

  1. #1
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    integration

    \int_0^\infty (\frac{k}{\lambda})(\frac{x}{\lambda})^{k-1} e^{-(\frac{x}{\lambda})^{k}}dx;    k and \lambda are positive

    My first instinct was to use integration by parts but this ends up looping back on itself infinitely. I'm struggling to see some kind of pattern I can play with in the repetition.
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    Quote Originally Posted by Rubberduckzilla View Post
    \int_0^\infty (\frac{k}{\lambda})(\frac{x}{\lambda})^{k-1} e^{-(\frac{x}{\lambda})^{k}}dx;  k and \lambda are positive

    My first instinct was to use integration by parts but this ends up looping back on itself infinitely. I'm struggling to see some kind of pattern I can play with in the repetition.
    Try reading this: Gamma function - Wikipedia, the free encyclopedia
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  3. #3
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    Hello,

    Substitute t=x/\lambda and then see this : Gamma function - Wikipedia, the free encyclopedia
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    The question is related to a probability distribution function i believe. So this integral should = 1
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  5. #5
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    Quote Originally Posted by Rubberduckzilla View Post
    The question is related to a probability distribution function i believe. So this integral should = 1
    Yes, we all realise that. But your question was how to do the integration.
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