# 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

I, KSmrq, the copyright holder of this work, hereby publishes it under the following licenses:
 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.