75 lines
1.5 KiB
TeX
75 lines
1.5 KiB
TeX
\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\usepackage{qrcode}
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\author{Benjamin Bertrand}
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\title{Integrale et Primitives - Cours}
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\date{novembre 2020}
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\pagestyle{empty}
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\begin{document}
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\maketitle
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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}{|m{4cm}|m{4cm}|}
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\hline
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\rowcolor{highlightbg}
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Fonction $f$ & Primitives $F$ \\
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\hline
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$a$ & $ax$ \\
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\hline
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$x$ & $\frac{1}{2}x^2$ \\
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\hline
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$x^2$ & $\frac{1}{3}x^3$ \\
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\hline
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$x^3$ & $\frac{1}{4}x^4$\\
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\hline
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$x^n$ & $\frac{1}{n+1}x^{n+1}$\\
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\hline
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$\frac{1}{x^2}$ & $\frac{-1}{x}$\\
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\hline
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$\cos(x)$ & $\sin(x)$\\
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\hline
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$\sin(x)$ & $-\cos(x)$\\
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\hline
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& \\
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\hline
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& \\
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\hline
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\end{tabular}
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\end{center}
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\paragraph{Exemples:}%
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Calculs des primitives des fonctions suivantes
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\[
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f(x) = 3x^2 - x + 5 \qquad \qquad F(x) =
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\]
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\[
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g(x) = \frac{3}{x^2} + \cos(x) \qquad \qquad G(x) =
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\]
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\[
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z(t) = 4t^5 - \sin(x) \qquad \qquad Z(t) =
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\]
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\envideo{https://video.opytex.org/videos/watch/cc688f48-2e83-46a2-8c81-0e67f300a37b}{Les exemples traités}
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\section{Calculer une primitive}
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\paragraph{Exemples:}%
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Calcul de la quantité suivante
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\[
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\int_0^{15} -0,2x^2 + 3x \; dx=
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\]
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\envideo{https://video.opytex.org/videos/watch/1ebc9f06-011f-48f2-b9c9-1297ef5a6634}{Reprendre le calcul de l'exemple et reproduire le graphique}
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\end{document}
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