Noun
Riemann sum (plural Riemann sums)
English Wikipedia has an article on:Riemann sumWikipedia
(mathematics) A certain kind of approximation of an integral by a finite sum that is calculated by dividing the interval of integration into smaller sub-intervals and summing sample values of the integrand inside those sub-intervals multiplied by their lengths.
A better approach replaces the rectangles used in a Riemann sum with trapezoids. Source: Internet
Then, by carefully choosing the new tags, we can make the value of the Riemann sum turn out to be within ε of either zero or one our choice! Source: Internet
The Riemann sum can be made as close as desired to the Riemann integral by making the partition fine enough. citation One important requirement is that the mesh of the partitions must become smaller and smaller, so that in the limit, it is zero. Source: Internet
The Riemann sum of with respect to the tagged partition together with is citation; citation Each term in the sum is the product of the value of the function at a given point, and the length of an interval. Source: Internet
These approaches based on the real number system are the ones most common today, but alternative approaches exist, such as a definition of integral as the standard part of an infinite Riemann sum, based on the hyperreal number system. Source: Internet
This will make the value of the Riemann sum at least 1−ε. Source: Internet