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==Riemann intergral==

==Riemann intergral==

As a geometric interpretation of the integral of the area of a curve the Riemann integral consist 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 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 sums become the intergral. If the approach the same value then the integral exists, otherwise it is undefined.

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 sums become the integral. If they approach the same value then the integral exists, otherwise it is undefined.

==Lebesgue Intergral==

==Lebesgue Intergral==

The Lebesgue intergral is usually introduced in late university or early postgraduate mathematics. It is nievely discribed as rotating the Reimann intergral, in that it is the range instead of the domain that is partioned. An understanding of [[measure theory]] is required to understand this techniques.

The Lebesgue intergral is usually introduced in late university or early postgraduate mathematics. It is naively described as rotating the Reimann intergral, in that it is the range instead of the domain that is partioned. An understanding of [[measure theory]] is required to understand this techniques.

==See Also==

==See Also==