An integral inequality

  • Thread starter tghg
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  • #1
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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.
 
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Answers and Replies

  • #2
HallsofIvy
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Have you tried anything? In particular, have you selected some simple monotonically decreasing function, such as [itex]f(x)= \frac{1}{x}[/itex] and calculated those two values?
 
  • #3
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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.
 

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