Changes

==Riemann integral==

==Riemann integral==

As a geometric interpretation of the integral of the [[area]] of a curve, the Riemann integral consists of dividing the area under the curve of the function into rectangles. The [[domain]] of the function is partioned into N segments of width <math>\frac{b-a}{N}</math>. The height of the segment is dependent on which side of the rectangle is taken. The lower sum takes the lower side of the rectangle, the upper sum the higher side of the rectangle. In the [[limit]] of <math>N\rightarrow\infty</math> these two [[series (mathematics)|series]] become the integral. If they approach the same value then the integral exists, otherwise it is undefined.

The Riemann integral is a geometric interpretation [[area]] under a curve (also called the [[integral]]), the Riemann integral consists of dividing the area under the curve of the function into smaller slices.  These do not necessarily have to be rectangles (for example, [[trapezoids]] or even [[parabolas]]), but in most cases

 

The [[domain]] of the function is partioned into N segments of width <math>\frac{b-a}{N}</math>. The height of the segment is dependent on which side of the rectangle is taken. The lower sum takes the lower side of the rectangle, the upper sum the higher side of the rectangle. In the [[limit]] of <math>N\rightarrow\infty</math> these two [[series (mathematics)|series]] become the integral. If they approach the same value then the integral exists, otherwise it is undefined.

==Lebesgue Integral==

==Lebesgue Integral==