2020-2021/TST_sti2d/04_Integrale_et_Primitives/2B_formulaire.tex

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2020-11-19 13:11:49 +00:00
\documentclass[a4paper,10pt]{article}
\usepackage{myXsim}
\author{Benjamin Bertrand}
\title{Integrale et Primitives - Cours}
\date{novembre 2020}
\pagestyle{empty}
\begin{document}
\maketitle
\setcounter{section}{2}
\section{Formulaire des primitives}
\begin{center}
\begin{tabular}{|m{4cm}|m{4cm}|}
\hline
\rowcolor{highlightbg}
Fonction $f$ & Primitives $F$ \\
\hline
$a$ & $ax$ \\
\hline
$x$ & $\frac{1}{2}x^2$ \\
\hline
$x^2$ & $\frac{1}{3}x^3$ \\
\hline
$x^3$ & $\frac{1}{4}x^4$\\
\hline
$x^n$ & $\frac{1}{n+1}x^{n+1}$\\
\hline
$\frac{1}{x^2}$ & $\frac{-1}{x}$\\
\hline
$\cos(x)$ & $\sin(x)$\\
\hline
$\sin(x)$ & $-\cos(x)$\\
\hline
& \\
\hline
& \\
\hline
\end{tabular}
\end{center}
\paragraph{Exemples:}%
Calculs des primitives des fonctions suivantes
\[
f(x) = 3x^2 - x + 5 \qquad \qquad F(x) =
\]
\[
g(x) = \frac{3}{x^2} + \cos(x) \qquad \qquad G(x) =
\]
\[
z(t) = 4t^5 - \sin(x) \qquad \qquad Z(t) =
\]
\end{document}