<div class="dem">
\def{integer n=randint(2..6)}
\def{text liste= c<sub> 1</sub>(t)}
\for{i=2 to \n}{\def{text liste= \liste, c<sub> \i</sub>(t)}}
Faisons la dmonstration pour
  \(n=\n)\reload{<img src="gifs/doc/etoile.gif" alt="rechargez" width=
  "20" height="20">}. On a 
<center>
\if{\n=2} {\(
\int _{\mathcal C} \rm{grad} f.dM &= \int_a^b \left(
\frac{\partial f}
{\partial x}(c_1(t),c_2(t))c'_1(t)+\frac{\partial f}{\partial y}(c_1(t),c_2(t))c'_2(t)
\right) dt =  \int_a^b 
g'(t)
 dt
 = g(b)-g(a)
)}{
	\(\int _{\mathcal C}) grad \ f.dM =\( \int_a^b)
	(
D<sub>1</sub>(f)(\liste)c'<sub>1</sub>(t)
\for{i=2 to \n}{+D<sub>\i</sub>(f)(\liste)c'<sub>\i</sub>(t)}) dt =  \(\int_a^b 
g'(t)
 dt
 = g(b)-g(a))
}
	</center>
avec   \if{\n=2}{\(g(t)=f(c_1(t),c_2(t)))}{g(t)=f(\liste)} .
</div>  