## cinar Group Title Let f be a continuous and bounded function on [a,b] such that if one year ago one year ago

1. cinar Group Title

2. cinar Group Title

any idea?

3. satellite73 Group Title

not really,but it kind of looks like a set up for integrating by parts

4. cinar Group Title

I guess so..

5. cinar Group Title

F'(x)=f(x) so we can say F'(t)=f(t) right..

6. satellite73 Group Title

that is what i was thinking, yes

7. satellite73 Group Title

maybe not exactly what you want, but you would get something like $$gF-\int f g'$$

8. cinar Group Title

$\lim_{b \rightarrow} \int\limits_{0}^{b }G(t)F'(t)dt=$

9. cinar Group Title

I guess enough to show that $\int\limits f g'$ is convergent

10. satellite73 Group Title

first part is no problem, since $$\lim_{t\to \infty}g(t)=0$$ and $$\int_a^\infty f(t)$$ is bounded

11. satellite73 Group Title

yeah you hit the nail on the head, and frankly i don't see why that is true, so this might be the wrong approach

12. satellite73 Group Title

because all you know about $$g'$$ is that $$g'\leq 0$$

13. satellite73 Group Title

does this come in a section after some theorem or lemma that maybe you are supposed to use?

14. cinar Group Title

no, this is homework, but prof gave the hint and said that you should use integration by part..

15. satellite73 Group Title

well then i guess this is the right approach!

16. cinar Group Title