70 lines
1.5 KiB
TeX
70 lines
1.5 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Tableau des primitives- bilan}
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\tribe{Terminale Sti2d}
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\date{Septembre 2019}
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\pagestyle{empty}
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\geometry{left=10mm,right=10mm, top=10mm}
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\begin{document}
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\setcounter{section}{2}
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\section{Formulaire des primitives}
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\begin{center}
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\begin{tabular}{|c|C{4cm}|}
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\hline
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Fonction $f$ & Primitive $F$ \\
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\hline
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$a$ & $ax$\\
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\hline
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$ax$ & $\frac{1}{2}ax^2$\\
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\hline
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$ax^2$ & $\frac{1}{3}ax^3$\\
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\hline
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$ax^n$ ($n\neq-1$) & $\dfrac{1}{n+1} ax^{n+1}$\\
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\hline
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$\dfrac{1}{x^2}$ & $\dfrac{-1}{x}$\\
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\hline
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$e^x$ & $e^x$\\
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\hline
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\end{tabular}
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\end{center}
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\subsubsection*{Exemples}
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\afaire{Trouver des primitives de
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\[
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f(x) = 3x^2 - 4x + 1 \qquad g(x) = 5x^3 + 6x^2 + e^{x}
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\]
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}
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\subsection*{Propriété}
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Soient $f$, $g$ deux fonctions continues et $a$ un nombre réel. On note $F$ (respectivement $G$) une primitive de $f$ (respectivement $g$). Alors
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\begin{itemize}
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\item Une primitive de $x\mapsto a\times f(x)$ est $x\mapsto a \times F(x)$
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\item Une primitive de $x\mapsto g(x) + f(x)$ est $x\mapsto G(x) + F(x)$
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\end{itemize}
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\subsection*{Propriété}
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Soit $u(x)$ une fonction dérivable. Alors une primitive de
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\[
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x\mapsto u'(x) e^{u(x)}
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\]
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est
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\[
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x\mapsto e^{u(x)}
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\]
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\subsubsection*{Exemples}
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\afaire{Trouver des primitives de
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\[
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f(x) = 2x\times e^{x^2}
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\]
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}
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\end{document}
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