Any possible lower bound!

  • Thread starter ssd
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  • #1
ssd
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Main Question or Discussion Point

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.
 
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Answers and Replies

  • #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
 
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  • #3
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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.
 
  • #4
ssd
268
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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.
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.
 
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  • #5
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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.
 
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  • #6
ssd
268
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Better how? It's an exact antiderivative. What do you want?

edit: You can edit your posts, you know. :)
Sorry for the misunderstanding, by 'second' I meant the other problem.
Thanks again for the help though.
 
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