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{{Unreferenced|date=August 2010}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


The '''constant factor rule in integration''' is a dual of the [[constant factor rule in differentiation]], and is a consequence of the [[linearity of integration]]. It states that a constant factor within an [[integrand]] can be separated from the integrand and instead multiplied by the integral. For example, where k is a constant:
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


<math>\int k \frac{dy}{dx} dx = k \int \frac{dy}{dx} dx. \quad </math>
Registered users will be able to choose between the following three rendering modes:


== Proof ==
'''MathML'''
Start by noticing that, from the definition of [[integral|integration]] as the [[Inverse function|inverse]] process of [[derivative|differentiation]]:
:<math forcemathmode="mathml">E=mc^2</math>


:<math>y = \int \frac{dy}{dx} dx.</math>
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


Now [[product (mathematics)|multiply]] both sides by a [[Coefficient|constant]] ''k''. Since ''k'' is a constant it is [[not dependent on]] ''x'':
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


:<math>ky = k \int \frac{dy}{dx} dx. \quad \mbox{(1)}</math>
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


Take the [[constant factor rule in differentiation]]:
==Demos==


:<math>\frac{d\left(ky\right)}{dx} = k \frac{dy}{dx}.</math>
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


[[integral|Integrate]] with respect to ''x'':


:<math>ky = \int k \frac{dy}{dx} dx. \quad \mbox{(2)}</math>
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


Now from (1) and (2) we have:
==Test pages ==


:<math>ky = k \int \frac{dy}{dx} dx</math>
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
:<math>ky = \int k \frac{dy}{dx} dx.</math>
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


Therefore:
*[[Inputtypes|Inputtypes (private Wikis only)]]
 
*[[Url2Image|Url2Image (private Wikis only)]]
:<math>\int k \frac{dy}{dx} dx = k \int \frac{dy}{dx} dx. \quad \mbox{(3)}</math>
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
Now make a new differentiable [[function (mathematics)|function]]:
 
:<math>u = \frac{dy}{dx}.</math>
 
[[Substitution property of equality|Substitute]] in (3):
 
:<math>\int ku dx = k \int u dx.</math>
 
Now we can re-substitute ''y'' for something different from what it was originally:
 
:<math>y = u. \,</math>
 
So:
 
:<math>\int ky dx = k \int y dx.</math>
 
This is the constant factor rule in integration.
 
A [[special case]] of this, with ''k''=-1, yields:
 
:<math>\int -y dx = -\int y dx.</math>
 
{{DEFAULTSORT:Constant Factor Rule In Integration}}
[[Category:Integral calculus]]
 
 
{{mathanalysis-stub}}
 
[[ar:قاعدة العامل الثابت في التكامل]]
[[eo:Konstanta faktora regulo en integralado]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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