# Thread: Apostol proof

1. ## Apostol proof

I'm not sure about this proof of the integral of 2x^2+1 from the vol. 1 of Apostol...
for the case 2x^2+1, the inequality becomes
$\displaystyle \frac{2b^3}{3}-\frac{2b^3}{n}+\frac{bn^2}{3}+bn<A<\frac{2b^3}{3}+ \frac{2b^3}{n}+bn+\frac{bn^2}{3}$

so I'm not sure how to prove this, I can calculate this by the Fundamental Theorem
for the x^2 case you have 3 possibilities that
$\displaystyle A>,<=\frac{b^2}{3}$
but then this changes for the other case