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Integration : Mapping Smoothly (-inf, 2] to [0.1,0.9]

  1. Mar 27, 2015 #1

    Hepth

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    Gold Member

    I have an Integral that is convergent over the range (-inf, Lambda) where 0< Lambda < 1.

    I need to change variables to move this to (0.1, 0.9) in such a way that I do not introduce any poor behavior, such as asymptotes or discontinuities as it needs to be well behaved.

    Is there a standard practice for this, like when mapping to unit cube/square?

    The integral is like :

    ## \int_{-\infty}^{\Lambda} e^{3 x} (\Lambda - x)^3 P[x] dx ##

    where P[x] is some generic polynomial or unknown smooth function.

    Thanks for your help!

    -Hepth

    EDIT :
    I guess I can just use something like
    ## \Lambda + \frac{(t-\text{tp})}{t-\text{tm}}##
     
    Last edited: Mar 27, 2015
  2. jcsd
  3. Mar 27, 2015 #2

    Svein

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    Science Advisor

    Try [itex]u=\frac{0.8}{\Lambda x}+0.1[/itex].
     
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