Ratios of integrals and its derivatives

[luluarg]

Hi guys, I've been trying to figure out if this ratio is less than 1, can anyone help me? it involves the ratio of an integral over its derivative, times the ratio of a function over its cumulative function. So I get something like f(t)/F(t) * Int{from 0 to t} f(x)dx/F(t).
are there any rules on these ratios that may help me prove this is less than one for continuous and positive functions? Thanks!

 

[CompuChip]

Assuming that f(t) is the derivative of F(t), there seems to be an inconsistency between what you write in words and what you write in formulas. But if you want to make any estimate at all, what you could use is that on a compact interval, like [0, t] (t in R), the positive continuous function f(t) takes a maximum M.

 

[luluarg]

Thanks, and yes, I noted there is a typo (sorry about that). It should actually read f(t)/F(t) * Int{o,t}F(x)dx/F(t).