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Definition of integral

  1. Oct 11, 2006 #1
    If we define the Riemann Integral so:

    [tex] \sum_{i=0}^{\infty}f(X_i )(X_{i+1}-X_{i} [/tex]

    as a "play" what would happen if i define the integral so:

    [tex] \sum_{i=0}^{\infty}f(X_i )(X_{i+1}+X_{i})0.5 [/tex] (2)

    In the second definition we define the "mean value" of 2 consecutive points instead of the difference, the question is if 2 is related to the Riemann integral by some formula.

    P.D:= Do Bernoulli Polynomials exist in more than 1 dimension?..:confused: :confused:
  2. jcsd
  3. Oct 12, 2006 #2

    matt grime

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    No, we do not define the Riemann integral as that.

    If you were to put down what the Riemann integral really is, you'd see that you're idea above would calculate f/2.
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