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Any possible lower bound!

  1. Mar 27, 2007 #1

    ssd

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    Looking for some positive valued simple functions which are less than (or equal to) the following two integrals (given in the following post).By simple I mean that they may not involve integrals or imaginary components or some infinite series. Again, the functions may not be as simple as f(x) =0.

    Please find the integrals in the following post, as I could not fix the latex problem in this post.

    Thanks for any idea.
     
    Last edited: Mar 27, 2007
  2. jcsd
  3. Mar 27, 2007 #2

    ssd

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    The integrals as referred in the previous post are as follows:


    [tex] 1/ \int_{x}^{\infty}\frac {e^{-y}}{y}dy [/tex] , x>0

    [tex] 2/ \int_{x}^{\infty} y e^{-y}dy [/tex] , x>0
     
    Last edited: Mar 27, 2007
  4. Mar 27, 2007 #3
    The second one can be integrated to (exactly) [tex]e^{-x}(1+x)[/tex].

    In the first one you can replace the y in the denominator by [tex]e^y[/tex] which will give you an easy integral. It will be a pretty bad lower bound though.
     
  5. Mar 27, 2007 #4

    ssd

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    Thank you very much, I missed the substitution in that.
    EDIT: I also missed that it simply can also be done 'by parts'.

    What I thought was to replace y in the denominator by [tex]e^y/2[/tex] or [tex] e^{y-1}[/tex] in the other problem.
    Any better idea about the second?...EDIT: I mean the other, problem no.1.
     
    Last edited: Mar 27, 2007
  6. Mar 27, 2007 #5
    Better how? It's an exact antiderivative. What do you want?

    edit: You can edit your posts, you know. :) Click the EDIT button next to the QUOTE button.
     
    Last edited: Mar 27, 2007
  7. Mar 27, 2007 #6

    ssd

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    Sorry for the misunderstanding, by 'second' I meant the other problem.
    Thanks again for the help though.
     
    Last edited: Mar 27, 2007
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