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Math Help - Apostol proof

  1. #1
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    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
    \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
    A>,<=\frac{b^2}{3}
    but then this changes for the other case
    Last edited by mathnerd15; May 8th 2014 at 02:10 AM.
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