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\lhead{\footnotesize{\textsf{Lycée JANSON DE SAILLY\\ 11 février 2014}}} %gauche
\chead{\textsf{\textcolor{red}{\textbf{\textsc{contrôle \no 6}}}}} %centre
\rhead{\footnotesize{\textsf{T\textsuperscript{le} STI2D\\Durée 1 heure 30}}}%droit
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\lfoot{ \htmladdnormallink{\scriptsize{\textsf{\textsc{A. Yallouz (MATH@ES)}}}}{http://yallouz.arie.free.fr}}
  
\begin{document}



\exo

\medskip

Calculer la valeur exacte de chacune des intégrales suivantes :

\medskip

\begin{enumerate}[$A =$]
 
\item $\displaystyle \int_{\frac{\pi}{12}}^{\frac{\pi}{4}} \dfrac{\cos 2t}{2} \:\dd t$

\medskip
 
\item $\displaystyle  \int_{3}^{6} \dfrac{2}{x-2} \:\dd x$ 

\medskip

\item $\displaystyle{\int_{\frac{-\pi}{3}}^{\frac{\pi}{2}}   2\cos 3t +3\sin 2t  \:\dd t} $

\end{enumerate}
\bigskip

\exo

\medskip

Calculer la valeur exacte de chacune des intégrales suivantes :

\bigskip

\begin{enumerate}[$A =$]

\item $\displaystyle \int_{-2}^{1} \dfrac{2x+1}{x^2+x+5} \:\dd x$

\medskip

\item $\displaystyle \int_{0}^{\ln 2}  2\e^x \times \left(\e^x+1\right) \:\dd x$

\medskip

\item $\displaystyle{\int_{\frac{\pi}{4}}^{\frac{\pi}{3}}   \cos t \sin t  \:\dd t} $


\medskip

\item $\displaystyle\int_{\frac{1}{2}}^{2}   \dfrac{\ln x}{x}  \:\dd x$ 

\medskip

\item $\displaystyle\int_{\ln 2}^{\ln 3}   \dfrac{\e^x}{\e^{x}+1}  \:\dd x$
\end{enumerate}

\bigskip

\exo

\medskip

La courbe $\mathcal{C}_f$ tracée ci-dessous est la représentation graphique d'une fonction $f$ définie et dérivable sur $\R$. 
	
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On note $F$ une primitive de la fonction fonction $f$.

	\begin{enumerate}
	
		\item Une des trois courbes ci-dessous est la représentation graphique de la primitive $F$. 
		
		Déterminer la courbe associée à la fonction $F$. 
		
\medskip

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\item Donner une valeur approchée (en unité d'aire) de l'aire du domaine hachuré.
\end{enumerate}


\end{document}

