How Can Simple Functions Help Find Lower Bounds for Integrals?

[ssd]

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.

 

[ssd]

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


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

$$2/ \int_{x}^{\infty} y e^{-y}dy$$ , x>0

 

[Eighty]

The second one can be integrated to (exactly) $$e^{-x}(1+x)$$.

In the first one you can replace the y in the denominator by $$e^y$$ which will give you an easy integral. It will be a pretty bad lower bound though.

 

[ssd]

The second one can be integrated to (exactly) $$e^{-x}(1+x)$$.

In the first one you can replace the y in the denominator by $$e^y$$ 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 $$e^y/2$$ or $$e^{y-1}$$ in the other problem.
Any better idea about the second?...EDIT: I mean the other, problem no.1.

 

[Eighty]

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.

 

[ssd]

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.