File:Riemann sum convergence.png

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Summary

Description	Show convergence of Riemann sum for all sample position choices as intervals shrink
Date	4 July 2007
Source	self-made using text editor, rendered by GLIPS Graffiti
Author	KSmrq

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Comment

An example of Riemann sums for the integral $\int_{-2}^{2} \tfrac15 \left( \tfrac{1}{100}(322 + 3 x (98 + x (37 + x))) - 24 \frac{x}{1+x^2} \right) dx ,$ sampling each interval at right (blue), minimum (red), maximum (green), or left (yellow). Convergence of all four choices to 3.76 occurs as number of intervals increases from 2 to 10 (and implicitly, to ∞).

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Integral

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