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Weibull integral

  1. Mar 20, 2010 #1
    Can someone explain this..
    [tex]P(v)=\frac{\beta}{\eta}\intop_{0}^{v}\left(\frac{v}{\eta}\right)^{\beta-1}\exp\left(-\left(\frac{v}{\eta}\right)^{\beta}\right)dv=\intop_{0}^{x}e^{-x}dx\hphantom{}\; where\phantom{\:}x=\left(\frac{v}{\eta}\right)^{\beta}[/tex]

    Thanks !
  2. jcsd
  3. Mar 20, 2010 #2


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    It just seems like a change of variable, but beware your notation.
    In the first integral you use v both as the integration variable and in the upper limit of integration. In the second, x plays both those roles too. This is confusing.
    I'd call the integration variable v' in the first one, then just make a change of variable substitution.
  4. Mar 20, 2010 #3


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    In line with Galileo's comment, this is how you should write it:
    [tex]P(v)=\frac{\beta}{\eta}\intop_{0}^{v}\left(\frac{V}{\eta}\right)^{\beta-1}\exp\left(-\left(\frac{V}{\eta}\right)^{\beta}\right)dV=\intop_{0}^{x(v)}e^{-X}dX\hphantom{}\; where\phantom{\:}x(v)=\left(\frac{v}{\eta}\right)^{\beta}[/tex]
  5. Mar 20, 2010 #4
    Thanks !!
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