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Riemann sum

In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is in numerical integration, i.e., approximating the area of functions or lines on a graph, where it is also known as the rectangle rule. It can also be…

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Overview

Definition

Types of Riemann sums

Riemann summation methods

Connection with integration

Higher dimensions

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Riemann sum

Nodes34
Edges33
Triples74
Avg. degree1.94
Density0.058824
Components1

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Riemann sum

Top relations

related to Example · 7
Riemann sum → Because, It, Riemann, Riemann's, Taking, The, Therefore
related to Left rule · 6
Riemann sum → Delta, Doing, For, Riemann, The, This
related to Midpoint rule · 6
Riemann sum → Delta, For, Riemann, Summing, The, This
related to Right rule · 6
Riemann sum → Delta, Doing, For, Riemann, The, This
related to Connection with integration · 5
Riemann sum → Delta, For, Riemann, The, This
related to Definition · 5
Riemann sum → Delta, In, Let, One, Riemann
related to Three dimensions · 5
Riemann sum → Delta, Each, In, Riemann, The
related to Two dimensions · 5
Riemann sum → Delta, Each, In, Riemann, The
related to Arbitrary number of dimensions · 4
Riemann sum → An, Delta, Higher, Riemann
related to External links · 4
Riemann sum → Eric, MathWorld, Riemann, Weisstein

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Important terminology

riemann displaystyle sum right left sums rule function delta gives integral area partition value subintervals interval method frac one shapes

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Riemann sumis acertain kind of approximation of an integral by a finite sum0.90text
Riemann sumis amost accurate approach to the Riemann sum.Trapezoidal rule.mw-parser-output .hatnote0.90text
Riemann sumis amost accurate approach to the Riemann sum0.90text
the Trapezoidal rule or Simpson's rule.The example function has an easy-to-find anti-derivative so estimating the integral by Riemann sums is mostly an academic exerciseinstance ofright and left Riemann sums are often less accurate than more advanced techniques of estimating an integral0.80text
Riemann sumhas methodThe0.60section
Riemann sumhas methodRiemann0.60section
Riemann sumhas methodDelta0.60section
Riemann sumrelated to Arbitrary number of dimensionsHigher0.60section
Riemann sumrelated to Arbitrary number of dimensionsRiemann0.60section
Riemann sumrelated to Arbitrary number of dimensionsAn0.60section
Riemann sumrelated to Arbitrary number of dimensionsDelta0.60section
Riemann sumrelated to Connection with integrationFor0.60section

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