Image:Improper integral.svg

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Improper_integral.svg‎ (SVG file, nominally 420 × 420 pixels, file size: 5 KB)

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Summary

Description	Plot of 1/(sqrt(x)*(x+1)) from 0.093 to 3.0
Source	self-made using gnuplot with alterations to SVG (piecewise-Bézier replacement of function graph, area fill)
Date	2007-06-26
Author	KSmrq
Permission ( Reusing this image)	see below

Comment

Illustrate an improper Riemann integral,

$\int_{0}^{\infty} \frac{dx}{(x+1)\sqrt{x}} = \pi .$

The domain goes to infinity, and at zero so does the range. Thus the integral is improper in both senses, but has a well-defined value using limits.

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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled " GNU Free Documentation license".

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	Date/Time	Dimensions	User	Comment
current	21:36, 26 June 2007	420×420 (5 KB)	KSmrq	({{Information \|Description=Plot of 1/(sqrt(x)*(x+1)) from 0.093 to 3.0 \|Source=self-made using gnuplot with alterations to SVG (piecewise-Bézier replacement of function graph, area fill) \|Date=2007-06-26 \|Author= KSmrq }} == Comment == Il)

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Integral

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