If we define the Riemann Integral so:(adsbygoogle = window.adsbygoogle || []).push({});

[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?..

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# Definition of integral

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