Summary

DescriptionRiemann sum error.svg	English: Graph showing the value of the Riemann sum approximation to ${\displaystyle \int _{0}^{2}x^{2}\mathrm {d} x}$ (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	23 March 2013
Source	Own work  This W3C-unspecified diagram was created with Mathematica. Category:Unspec SVG created with Mathematica#00100302Riemann%20sum%20error.svg
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.