96 lines
2.2 KiB
TeX
96 lines
2.2 KiB
TeX
\documentclass[12pt,xcolor=table]{classPres}
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\title{Calculs d'intégrales}
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\date{Janvier 2020}
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\begin{document}
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\begin{frame}{Tableau des primitives}
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Retrouver les primitives de fonctions suivantes
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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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$a$ & \\
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\hline
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$ax$ & \\
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\hline
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$ax^2$ & \\
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\hline
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$ax^n$ ($n\neq-1$) & \\
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\hline
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$\frac{1}{x}$ & \\
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\hline
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$\cos(x)$ & \\
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\hline
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$\sin(x)$ & \\
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\hline
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\end{tabular}
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\end{center}
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\end{frame}
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\begin{frame}{Primitives}
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\begin{block}{Calculer les primitives}
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\begin{multicols}{2}
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\begin{enumerate}
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\item $f(x) = 2x + 1$
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\vspace{0.5cm}
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\item $g(t) = t^2-2t +2$
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\vspace{0.5cm}
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\item $h(x) = 2x(4x+1)$
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\item $i(x) = x + 1 + \frac{1}{x}$
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\vspace{0.5cm}
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\item $j(x) = 3x - \frac{2}{x}$
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\vspace{0.5cm}
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\item $k(x) = x^{10} + \frac{5}{x^2}$
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\end{enumerate}
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\end{multicols}
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\end{block}
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\begin{block}{Calculer les primitives avec les contraintes}
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\begin{enumerate}
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\item $f(x) = 2x + 1$ et $F(0) = 5$
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\vspace{0.5cm}
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\item $g(t) = t^2-2t +2$ et $G(10) = 0
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\vspace{0.5cm}
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\end{enumerate}
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\end{block}
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\vfill
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\end{frame}
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\begin{frame}{Intégrales}
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\begin{block}{Calculer les intégrales}
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\[
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A = \int_2^3 x^3+4x^2+x+1 dx
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\qquad \qquad
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B = \int_2^3 t^5 - 9 dt
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\]
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\vfill
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\[
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C = \int_4^6 3x(x-1) dx
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\qquad \qquad
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D = \int_4^6 2x + 5\frac{1}{x} dx
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\]
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\vfill
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\[
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E = \int_{\pi}^{5\pi} 2\cos(x) dx
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\qquad \qquad
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F = \int_{0}^{\frac{\pi}{2}} 2\cos(x) + \sin(x) dx
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\]
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\vfill
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\end{block}
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\vfill
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\end{frame}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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