Riemann sum

English Etymology Named after Bernhard Riemann, a German mathematician. Noun en 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. Usage notes In mathematical terms, let be a function defined on a closed interval . Let be partitioned by points , and denote the length of the th subinterval , i.e. . A Riemann sum of is defined as , where is an arbitrary point in the th subinterval, i.e. . Translations kind of approximation of an integral French: fr somme de Riemann f Polish: pl suma Riemanna f Portuguese: pt soma de Riemann f Spanish: es suma de Riemann f See also en Riemann integral