How Does Monotonicity Affect Integral Inequalities?

[tghg]

Homework Statement

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]

Homework Equations

none

The Attempt at a Solution

Maybe the second mean value thereom of integral is helpful.

 

[HallsofIvy]

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?

 

[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.