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% ########################### MES PARAMETRES ##############################################################
\def\monnumero{ }
\def\madate{ Mars 2026 }
\def\maclasse{ T\textsuperscript{erm} Spé maths}
% ########################### MES PARAMETRES ##############################################################

% en-tête
\lhead{\footnotesize{\textsf{Lycée Schuman Perret\\ \madate}}} %gauche
\chead{\textsf{\textcolor{red}{\textbf{\textsc{SERIE D'EXERCICES SUR L'INTEGRATION}}}}} %centre
\rhead{\footnotesize{\textsf{\maclasse}}}%droit
%pied de page
\rfoot{\scriptsize{\textsf{Page~\thepage{}~sur~\pageref{LastPage}}}}
\lfoot{ {\scriptsize{\textsf{\textsc{Stéphane Le Méteil }}}}}


\newcounter{nexo}           % déclaration du numéro d'exo
\setcounter{nexo}{0}        % initialisation du numero

\newcommand{\exo}{
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  \bigskip\par{\textsf{\textbf{\textcolor{blue}{{\small{EXERCICE \; \arabic{nexo}}}}}}\quad}}

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\begin{document}
%\everymath{\displaystyle}
%\doublespacing



\exo Calculer $\ds\int_{-3}^4 f(t)dt$ dans chacun des cas suivants :

\begin{multicols}{2}
\begin{enumerate}[a)]

\item ~

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    \psaxes[showorigin=false,labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2]{->}(0,0)(-3.86,-1.78)(5.72,3.36)
    \psline[linewidth=0.5pt,linecolor=blue](-3.,1.)(-1.,3.)(2.,3.)(4.,0.)
    \end{pspicture*}

\item ~

	\psset{xunit=0.75cm,yunit=0.75cm,algebraic=true,dimen=middle,dotstyle=o,dotsize=5pt 0,linewidth=0.5pt,arrowsize=3pt 2,arrowinset=0.25}
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\item ~

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\item ~

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\end{enumerate}

\end{multicols}

\exo Calculer les dérivées des fonctions suivantes.

\begin{multicols}{2}
\begin{enumerate}[1)]

\item $f(x)  =x^3+4x+2$

\item $f(x)  =(3x+1)^2$

\item $f(x)  = (-4+x)^3$

\item $f(x)  = \dfrac{1}{2x+1}$

\item $f(x)  = \dfrac{3}{5x^2-1}$

\item $f(x)  = \sqrt{7x+1}$

\item $f(x)  = 2\sqrt{5-2x}$

\item $f(x)  = e^{2x+2}$

\item $f(x)  = 7e^{3x-2}$

\item $f(x)  = \ln(2x+2)$

\item $f(x)  = \ln(3x-2)$

\item $f(x)  =\cos(4x+1)$

\item $f(x)  = 5\sin(4x+1)$

\item $f(x)  = x\times e^x$

\end{enumerate}

\end{multicols}

\exo Calculer des primitives des fonctions suivantes.

\begin{multicols}{2}
\begin{enumerate}[1)]

\item $f(x)  = 4x+2$

\item $f(x)  = 5x^3$

\item $f(x)  = (x+1)(x-1)$

\item $f(x)  = x^3+4x+2$

\item $f(x)  = (3x+1)^2$

\item $f(x)  = (4-x)^3$

\item $f(x)  = \dfrac{1}{2x+1}$

\item $f(x)  = \dfrac{3x}{5x^2+1}$

\item $f(x)  = \sqrt{x}$

\item $f(x)  = e^{2x+2}$

\item $f(x)  = 7e^{-3x}$

\item $f(x)  = \cos(4x+1)$

\item $f(x)  = 5\sin(4x+1)$

\item $f(x)  = x\times e^x$

\end{enumerate}

\end{multicols}

\end{document} 