I want to show that . I'm not sure where to begin on this. It is an excercise in a chapter about the Fundamental Theorem of calculus. Any suggestions?

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- November 10th 2009, 10:09 AMadkinsjrFundamental Theorem
I want to show that . I'm not sure where to begin on this. It is an excercise in a chapter about the Fundamental Theorem of calculus. Any suggestions?

- November 10th 2009, 11:12 AMtonio
- November 10th 2009, 11:58 AMadkinsjr
I'm not sure what you mean. Are trying to say that is the same as ???

(Thinking) I don't see that

I can see how the entire innequality is obviously true. I just don't see how to prove it formally. And yes, .

The excercise appears in a chapter on the fundamental theorem. One of the properties of integrals is

Where and is in .

This property is used in one of the proofs of the fundamental theorem. - November 10th 2009, 01:59 PMJG89
You don't need the FTC for this. The left hand inequality is obviously true for non-negative x. For the right hand inequality, square both sides. You get .

You know that if c is a positive number greater than or equal to 1, then , right? So just put c = 1 + x^3 - November 10th 2009, 02:20 PMadkinsjr
That's what I was thinking. It's a very obvious inequality, I just thought it was strange that it was an excercise in a chapter on the fundamental theorem. I thought that perhaps someone might see a connetion between the two, because I don't. It's a very obvious algebraic statement.

- November 10th 2009, 06:08 PMtonio