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Reverse integrals

  1. Jan 14, 2014 #1
    I need to find a function f(x) such that

    [tex]\int_{-\infty}^{100+10n} (f(x)) dx = 1-0.1^n[/tex]

    for n=1,2,3,4,5,6...∞. How would I go about this? It must be exponential in some way I'm guessing?

    This is not a homework problem. I don't just want the answer. I want guidance on this type of problem and function, but please from someone with an idea of how to answer this particular case too ...
  2. jcsd
  3. Jan 14, 2014 #2


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    Replace (100+10n) by a real variable (y). Take the derivative of both sides, this will give you an expression for f(y) if it exists. It will be an exponential.
    Last edited: Jan 14, 2014
  4. Jan 14, 2014 #3
    So y=100+10n, n = 1/10(y-100) = (1/10)y-10.

    Now what? I need to bear the integral limits (-∞ to y) in mind...
  5. Jan 15, 2014 #4


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    0.1n = 0.1(y-100)/10 = exp((y-100)ln(0.1)/10). Now take the derivatives of both sides to get f(y) = .
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