I'm not sure what you mean. Are trying to say that is the same as ???
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.
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
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.