File:Riemann sum error.svg

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Original file(SVG file, nominally 242 × 167 pixels, file size: 118 KB)

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Summary

Description
English: Graph showing the value of the Riemann sum approximation to (using right endpoint as rectangle height) as the number of rectangles increases. It approaches the blue line y=8/3, the actual value of the definite integral. Source below.
Date
Source Own work
 
This W3C-unspecified diagram was created with Mathematica.
Author User:Dcoetzee

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Source

Mathematica code:

LogLinearPlot[{8/3, 8/3 + 4/Floor[n] + 4/(3 Floor[n]^2)}, {n, 1, 
  1000}, PlotRange -> {2, 5}, AxesStyle -> FontSize -> 14, 
 PlotPoints -> 1000, Exclusions -> None, 
 Ticks -> {Table[10^i, {i, 0, 3}], Automatic}]

The plot was then edited in Inkscape to use Liberation Serif and add axes labels.

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23 March 2013

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Date/TimeThumbnailDimensionsUserComment
current11:30, 23 March 2013Thumbnail for version as of 11:30, 23 March 2013242 × 167 (118 KB)Dcoetzee{{Information |Description ={{en|1=Graph showing the value of the Riemann sum approximation to <math>\int_0^2 x^2 \mathrm{d}x</math> (using right endpoint as rectangle height) as the number of rectangles increases. It approaches the blue line y=8/3,...

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