Riemann sum

Etymology
Named after Bernhard Riemann, a German mathematician.

Noun

 * 1)  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.

Usage notes
In mathematical terms, let $$f $$ be a function defined on a closed interval $$[a,b]$$. Let $$[a,b]$$ be partitioned by points $$a=x_0<x_1<x_2<\cdots<x_{n-1}<x_n=b$$, and $$\Delta x_k$$ denote the length of the $$k$$th subinterval $$[x_{k-1},x_k]$$, i.e. $$\Delta x_k=x_k-x_{k-1} $$. A Riemann sum $$S$$ of $$f $$ is defined as $$S = \sum_{k=1}^{n} f(x_k^*)\, \Delta x_k$$, where $$x_k^*$$ is an arbitrary point in the $$k$$th subinterval, i.e. $$x_k^*\in[x_{k-1},x_k]$$.