(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

My question is on the last bit of Apostol's proof, in his book Calculus Vol I 2nd ed, where he shows that the area under the parabola = b[tex]^{3}[/tex]/3 where b is the base of the rectangle enclosing the parabola.

The bit I am confused about is where his contradiction n[tex]\geq[/tex]b[tex]^{3}[/tex]/(A-b[tex]^{3}[/tex]/n) came from?

I know this is impossible for anyone to solve unless they own the book... However, please please could someone understand my frustration and also the lack of knowledge of knowing Latex enough to replicate the problem. If you own the book, please could you help me?

I would greatly appreciate help!

2. Relevant equations

3. The attempt at a solution

I have tried various approaches in trying to attain the n[tex]\geq[/tex]b[tex]^{3}[/tex]/(A-b[tex]^{3}[/tex]/n), however, I have not been successful either way. Sorry, it might not seem like proper attempts have been made, but I have tried, and I have constantly failed to gain it.

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# Apostol's Archimedes area proof for a parabola

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