# Definition of integral

1. Oct 11, 2006

If we define the Riemann Integral so:

$$\sum_{i=0}^{\infty}f(X_i )(X_{i+1}-X_{i}$$

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

$$\sum_{i=0}^{\infty}f(X_i )(X_{i+1}+X_{i})0.5$$ (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?..

2. Oct 12, 2006

### matt grime

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.