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File:Riemann sum error.svg

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

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.
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This W3C-unspecified diagram was created with Mathematica.
Author User:Dcoetzee

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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
current17:30, 23 March 2013Thumbnail for version as of 17:30, 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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