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+\usepackage{tkz-fct} + +\author{} +\title{} +\date{} + +\begin{document} +\begin{frame}{Aire et intégrale} + Soit $f(x) = x-ln(x)$ et $g(x)=\dfrac{x^2}{3}-\dfrac{ln(x)}{5}$ deux fonctions définies sur $\intOO{0}{+\infty}$. + \begin{itemize} + \item Vérifier que $F$ et $G$ sont des primitives de $f$ et $g$. + \[ F(x) = \frac{1}{2}x(x-2ln(x) +2) \] + \[ G(x) = \frac{1}{45}x(5x^2-9ln(x)+9) \] + \item Calculer les 2 quantités suivantes et interpréter ces quantités + \[\int^{0.1}_{2.67} f(x)dx \qquad \int^{0.1}_{2.67} g(x)dx\] + \end{itemize} +\end{frame} + +\end{document} diff --git a/PreStSauveur/Tsti2d/Integrale/index.rst b/PreStSauveur/Tsti2d/Integrale/index.rst new file mode 100644 index 0000000..4f9f4ad --- /dev/null +++ b/PreStSauveur/Tsti2d/Integrale/index.rst @@ -0,0 +1,41 @@ +Fin du chapitre intégrale avec les Tsti2d en remplacement à Saint Claude +######################################################################## + +:date: 2019-04-07 +:modified: 2019-04-07 +:tags: Integrale +:category: TSTI2D +:authors: Bertrand Benjamin +:summary: Situations à modéliser avec des suites pour les Tsti2d (septembre 2018) + +Étape 1: Lien primitive intégrale et aire entre 2 courbes +========================================================= + +Quelques calculs de primitives comme échauffement. (/!\ à choisir) +Exercices (type 57p218): f(x) = x-ln(x)/2 et g(x)=x**2/3-ln(x)/5 + - Vérification que F(x) et G(x) sont bien des primitives + - Calcul des intégrales entre 0.1 et 2.67. + - Interprétation et calcul de l'aire entre les 2 courbes. + +Étape 2: Encadrement le l'aire d'une fonction +============================================= + +Quelques calculs de primitives comme échauffement. +Justification d'un encadrement à travers une lecture graphique (68p220). + +Cours(?): Algo pour approximer une l'aire sous une courbe avec des rectangles. +/!\ à faire!!!! + +Étape 3: Fonction périodique et valeur moyenne +============================================== + +Primitives de fonction des exercices 77 (x-7+4/(x-3)) et 79 (900te**(-0.1*(t-2))). +Cours: définition de la valeur moyenne. +Calcul des valeurs moyennes des fonctions. + +Calculs de valeurs moyenne sur les périodes de fonctions périodiques (exo 80 - sin(x); cos**2*sin) + +Étape 4: Sujet type bac +======================= + +Exo 2 Bac 2018 Antille-Guyanne diff --git a/PreStSauveur/Tsti2d/Suites/index.rst b/PreStSauveur/Tsti2d/Suites/index.rst index 02924c0..a139115 100644 --- a/PreStSauveur/Tsti2d/Suites/index.rst +++ b/PreStSauveur/Tsti2d/Suites/index.rst @@ -4,7 +4,7 @@ Modélisation avec des suites avec les Tsti2d en remplacement à Saint Claude :date: 2018-09-11 :modified: 2018-09-11 :tags: Suites, Modelisation -:category: TESL +:category: TSTI2D :authors: Bertrand Benjamin :summary: Situations à modéliser avec des suites pour les Tsti2d (septembre 2018)