\begin{exercice*}Dans chacun des cas suivants, exprimer l'aire du
  domaine colorié sous la forme d'une intégrale.

 (On ne demande pas de calculer l'intégrale.)
\begin{colenumerate}{2}
 \item \hfill\\
 \begin{tikzpicture}[general, xscale=0.6, yscale=0.6]
   \draw [quadrillage] (-1,-1) grid (4,4);
   \draw (-1,0)--(4,0);
   \draw (0,-1)--(0,4);
   \draw[color=black] (0,0) node[below left] {$O$};
   \draw[ultra thick, ->] (0,0)--(1,0);
   \draw[ultra thick, ->] (0,0)--(0,1);
   \draw[color=black] (0.5,0) node[below] {$\overrightarrow{i}$};
   \draw[color=black] (0,0.5) node[left] {$\overrightarrow{j}$};
   \draw[domain=-1:3.2, color=B2, smooth] plot(\x,{(\x-2)*\x*(\x+2)/5});
   \draw (2.5,-0.5) [color=B2] node{{\boldmath $\mathscr{C}_f$}};
   \draw[domain=-0.37:4, color=D1, smooth] plot(\x,{ln(1+\x)/ln(4)*3});
   \draw (1.3,2.5) [color=D1] node{{\boldmath $\mathscr{C}_g$}};
   \fill[color=C1, opacity=0.2] plot[domain=0:3] (\x,{ln(1+\x)/ln(4)*3})
   									-- plot[domain=3:0] (\x,{(\x-2)*\x*(\x+2)/5});
 \end{tikzpicture}
 
 \item \hfill\\
 \begin{tikzpicture}[general, xscale=0.6, yscale=0.6]
   \draw [quadrillage] (-3,-1) grid (2,4);
   \draw (-3,0)--(2,0);
   \draw (0,-1)--(0,4);
   \draw[color=black] (0,0) node[below left] {$O$};
   \draw[ultra thick, ->] (0,0)--(1,0);
   \draw[ultra thick, ->] (0,0)--(0,1);
   \draw[color=black] (0.5,0) node[below] {$\overrightarrow{i}$};
   \draw[color=black] (0,0.5) node[left] {$\overrightarrow{j}$};
   \draw[domain=-2.63:1.66, color=B2, smooth] plot(\x,{(\x-1)*\x*(\x+2)/2+2});
   \draw (-1.5,3.5) [color=B2] node{{\boldmath $\mathscr{C}_f$}};
   \draw[domain=-2.47:1.8, color=D1, smooth] plot(\x,{(\x)^2*(\x-1)*(\x+2)/5+2});
   \draw (-1.5,1) [color=D1] node{{\boldmath $\mathscr{C}_g$}};
   \fill[color=C1, opacity=0.2] plot[domain=-2:1] (\x,{(\x-1)*\x*(\x+2)/2+2})
   									-- plot[domain=1:-2] (\x,{(\x)^2*(\x-1)*(\x+2)/5+2});
 \end{tikzpicture}
 
 \item \hfill\\
 \begin{tikzpicture}[general, xscale=0.75, yscale=0.75]
   \draw [quadrillage] (-2,-2) grid (2,2);
   \draw (-2,0)--(2,0);
   \draw (0,-2)--(0,2);
   \draw[color=black] (0,0) node[below left] {$O$};
   \draw[ultra thick, ->] (0,0)--(1,0);
   \draw[ultra thick, ->] (0,0)--(0,1);
   \draw[color=black] (0.5,0) node[below] {$\overrightarrow{i}$};
   \draw[color=black] (0,0.5) node[left] {$\overrightarrow{j}$};
   \draw[domain=-2:2, color=B2, smooth] plot(\x,{2*\x*exp(-\x*\x)});
   \draw (1.5,-0.5) [color=B2] node{{\boldmath $\mathscr{C}_f$}};
   \draw[domain=-2:2, color=D1, smooth] plot(\x,{\x*(2*exp(-1))});
   \draw (1.5,1.5) [color=D1] node{{\boldmath $\mathscr{C}_g$}};
   \fill[color=C1, opacity=0.2] plot[domain=-1:1] (\x,{\x*(2*exp(-1))})
   									-- plot[domain=1:-1] (\x,{2*\x*exp(-\x*\x)});
 \end{tikzpicture}
 
 \item \hfill\\
 \begin{tikzpicture}[general, xscale=1.5, yscale=0.6]
   \draw [quadrillage][xstep = 0.5, ystep = 1, line width = 0.1mm] (-1,-2) grid (1,3);
   \draw [quadrillage] (-1,-2) grid (1,3);
   \draw (-1,0)--(1,0);
   \draw (0,-2)--(0,3);
   \draw[color=black] (0,0) node[below left] {$O$};
   \draw[ultra thick, ->] (0,0)--(1,0);
   \draw[ultra thick, ->] (0,0)--(0,1);
   \draw[color=black] (0.5,0) node[below] {$\overrightarrow{i}$};
   \draw[color=black] (0,0.5) node[left] {$\overrightarrow{j}$};
   \draw[domain=-1:1, color=B2, smooth] plot(\x,{(2*\x)^2-1});
   \draw (-0.75,2.5) [color=B2] node{{\boldmath $\mathscr{C}_f$}};
   \fill[color=C1, opacity=0.2] (-0.5,0) -- (1,0)
   								-- plot[domain=1:-0.5] (\x,{(2*\x)^2-1});
 \end{tikzpicture}
\end{colenumerate}

\begin{corrige}
\begin{enumerate}
 \item $\displaystyle{\int_0^3} (g-f)(x) \mathrm{d}x$
 \item $\displaystyle{\int_{-2}^0} (f-g)(x) \mathrm{d}x
 				+ \displaystyle{\int_0^1} (g-f)(x) \mathrm{d}x$
 \item $\displaystyle{\int_{-1}^0} (g-f)(x) \mathrm{d}x
 				+ \displaystyle{\int_0^1} (f-g)(x) \mathrm{d}x$
 \item $\displaystyle{\int_{-0,5}^{0,5}} (-f)(x) \mathrm{d}x
 				+ \displaystyle{\int_{0,5}^1} f(x) \mathrm{d}x$
\end{enumerate}
\end{corrige}
\end{exercice*}

