File:Integrale double partie decimale de x.png
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Summary
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| Description |
∫∫(t - E(t ))·dt 2 English: Antiderivative of the antiderivative of the decimal part function ; this is an example of function that can be derivated once but not twice. Made with Scilab
Français : Intégrale double de la fonction partie décimale ; c'est un exemple de fonction continue dérivable une fois mais pas deux. Réalisé avec Scilab |
| Date | |
| Source | Own work |
| Author | Christophe Dang Ngoc Chan (cdang) |
Scilab source
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This media was created with Scilab, a free open-source software. Here is a listing of the Scilab source used to create this file. |
clear;clf;
// fonction initiale
deff('y=f(x)','y=x-int(x)')
// domaine d'étude
pas=0.01;
X=0:pas:2';
NX=size(X);nx=NX(1,2);
// sous-domaines pour le tracé
X1=0:pas:1-pas';
X2=1+pas:pas:2-pas';
// intégrale première
deff('y=f1(x)','y=0.5*(x-int(x))^2+0.5*int(x)')
Y1=feval(X,f1);
// intégrale seconde
Y2(1)=0
for i=2:nx
Y2(i)=Y2(i-1)+Y1(i);
end
// affichage
subplot(3,1,1)
plot2d(X1,f(X1),style=2)
plot2d(X2,f(X2),style=2)
axe=get('current_axes');
axe.x_location='middle'; axe.y_location='middle';
xtitle('f=x-E(x)','x','y')
subplot(3,1,2)
plot2d(X,Y1,style=2)
axe1=get('current_axes');
axe1.x_location='middle'; axe1.y_location='middle';
xtitle('intégrale de f','x','y')
subplot(3,1,3)
plot2d(X,Y2,style=2)
axe2=get('current_axes');
axe2.x_location='middle'; axe2.y_location='middle';
xtitle('intégrale double de f','x','y')
Licensing
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I, the copyright holder of this work, hereby publish it under the following licenses:
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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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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
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| This licensing tag was added to this file as part of the GFDL licensing update. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:24, 8 December 2005 | | 610 × 461 (4 KB) | Cdang (talk | contribs) | \int;\int;(''t''-''E''(''t''))·''dt''<sup>2</sup> Intégrale double de la fonction partie décimale ; c'est un exemple de fonction continue non dérivable. ---- Antiderivative of the antiderivative of the decimal part function ; this is an examp |
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