Reverse integrals

  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. mathman

    mathman 6,754
    Science Advisor
    Gold Member

    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. 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. mathman

    mathman 6,754
    Science Advisor
    Gold Member

    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) = .
Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?

Draft saved Draft deleted