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File:Improper integral.svg

Summary

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

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.

Licensing

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attribution share alike		 This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license.
Attribution: I, KSmrq
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
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Short title Improper integral
Image title Plot of 1/(sqrt(x)*(x+1)) from 0.093 to 3.0

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