Mathc initiation/Fichiers c : c74c05
Installer et compiler ces fichiers dans votre répertoire de travail.
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c01e.c |
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/* ---------------------------------- */
/* save as c1e.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fe.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*50;
double a = 0.;
double b = .5;
clrscrn();
printf(" With the Simpson's rule. (n = %d)\n\n"
" (%.3f\n"
" int( (%s) dx = %.6f\n"
" (%.3f\n\n\n\n",n, b, feq, simpson(f,a,b,n), a);
printf(" With the antiderivative of f.\n\n"
" F(x) = %s \n\n\n"
" F(%.3f) - F(%.3f) = %.6f \n\n\n", Feq, b,a, F(b)-F(a));
stop();
return 0;
}
/* ---------------------------------- */
Calculons l'intégrale avec la fonction simpson(f,a,b,n); puis avec sa primitive F(x).
Exemple de sortie écran :
With the Simpson's rule. (n = 100)
(0.500
int( (tanh(x)) dx = 0.120115
(0.000
With the antiderivative of f.
F(x) = ln( |cosh(x)| )
F(0.500) - F(0.000) = 0.120115
Press return to continue.
Calculons la primitive :
Calculer la primitive de
/ /
| tanh(x) dx = | sinh(x)/cosh(x) dx
/ /
________________________
/ sinh(x) dx | u = cosh(x) |
= | ----- | du = sinh(x) dx |
/ cosh(x) |______________________|
/ / 1 du
| tanh(x) dx = | -----
/ / u
= ln( |u| ) + c
= ln( |cosh(x)| ) + c