Mathc initiation/Fichiers c : c74c01
Apparence
Installer et compiler ces fichiers dans votre répertoire de travail.
c01a.c |
---|
/* ---------------------------------- */
/* save as c1a.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fa.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*50;
double a = -1;
double b = 1;
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)
(1.000
int( ((sec(x)) dx = 2.452382
(-1.000
With the antiderivative of f.
F(x) = ln( |sec(x)+tan(x)| )
F(1.000) - F(-1.000) = 2.452382
Press return to continue.
Calculons la primitive :
Calculer la primitive de
/ /
| sec(x) dx = | sec(x) * (1) dx
/ /
/ sec(x) + tan(x)
= | sec(x) * (-----------------) dx
/ sec(x) + tan(x)
___________________________________
/ sec(x)**2 + tan(x) * sec(x) | u = sec(x) + tan(x) |
= | (-----------------------------) dx |du = tan(x)*sec(x) + sec(x)**2 dx |
/ sec(x) + tan(x) |__________________________________|
/ /
| sec(x) dx = | 1/u du
/ /
= ln( |u| ) + c
= ln( |sec(x)+tan(x)| ) + c