# An integral inequality

1. Feb 14, 2007

### tghg

1. The problem statement, all variables and given/known data
suppose f(x) is monotonely decreasing and positive on [2,+∞),
please compare [∫f(t)dt]^2 and ∫[f(t)]^2dt,
here "∫ "means integrating on the interval [2,x]

2. Relevant equations
none

3. The attempt at a solution

Maybe the second mean value thereom of integral is helpful.

Last edited: Feb 14, 2007
2. Feb 14, 2007

### HallsofIvy

Staff Emeritus
Have you tried anything? In particular, have you selected some simple monotonically decreasing function, such as $f(x)= \frac{1}{x}$ and calculated those two values?

3. Feb 14, 2007

### tghg

In fact, yes!
But what I'm really eager to know is how to prove the conclusion.
Maybe when the x is large enough, [∫f(t)dt]^2 is larger.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook