Image:Riemann sum convergence.png

From Wikipedia, the free encyclopedia

Wikimedia Commons logo This is a file from the Wikimedia Commons. The description on its description page there is shown below.
Commons is a freely licensed media file repository. You can help.

[edit] Summary

Description

Show convergence of Riemann sum for all sample position choices as intervals shrink
Source

self-made using text editor, rendered by GLIPS Graffiti
Date

2007-07-04
Author

KSmrq
Permission
(Reusing this image)

see below

This graph image should be recreated using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is already available, please upload it. After uploading an SVG, replace this template with template {{Vector version available|new image name.svg}} in this image.

العربية | Български | Català | Česky | Dansk | Deutsch | English | Esperanto | Español | Français | 한국어 | Italiano | Magyar | Lietuvių | Nederlands | 日本語 | Polski | Português | Română | Русский | Suomi | Svenska | Türkçe | Українська | Tiếng Việt | मराठी | ‪中文(繁體)‬ | ‪中文(简体)‬ | +/-

[edit] 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 ∞).


[edit] Licensing

I, KSmrq, the copyright holder of this work, has published or hereby publishes it under the following licenses:
GNU head 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".

Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/-
Creative Commons License
Creative Commons Attribution iconCreative Commons Share Alike icon		 This file is licensed under the Creative Commons Attribution ShareAlike 2.5 License. In short: you are free to share and make derivative works of the file under the conditions that you appropriately attribute it, and that you distribute it only under a license identical to this one. Official license
You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current11:06, 4 July 20071,260×1,260 (66 KB)KSmrq ({{Information |Description=Show convergence of Riemann sum for all sample position choices as intervals shrink |Source=self-made using text editor, rendered by GLIPS Graffiti |Date=2007-07-04 |Author= KSmrq }} == Comment == An example of R)
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):