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Proof of an inequality

  1. Mar 16, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that


    where [tex]0=x_1<x_2<\cdots<x_{2n+1}=1[/tex] such that [tex]x_{k+1}-x_{k}<h[/tex] for [tex]1\le k\le 2n[/tex]

    2. Relevant equations

    How to prove? :-)

    3. The attempt at a solution

    I need to prove

  2. jcsd
  3. Mar 16, 2010 #2
    Draw a diagram. Each term in the sum corresponds to an approximation of the area under the graph in the interval [tex](x_{2k-1},x_{2k+1})[/tex]. For each interval, find the difference between
    [the approximation] and [the exact value for the area under the graph in the interval [tex](x_{2k-1},x_{2k+1})[/tex]]

    Add up the differences and you will get your result.
    Last edited: Mar 16, 2010
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