Image:Integrale double partie decimale de x.png

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[edit] Summary

\int;\int;(t-E(t))·dt²

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 example of function that can be derivated once but not twice

Auteur/author : Christophe Dang Ngoc Chan (cdang)

Réalisé avec/made with Scilab

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')

[edit] Licensing

I, the copyright holder of this work, have published or hereby publish it under the following license: 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)‬ | +/-

Les pages ci-dessous contiennent cette image :

• Dérivabilité
• Dérivée seconde