Mathc initiation/Fichiers c : c74c09
Installer et compiler ces fichiers dans votre répertoire de travail.
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c01i.c |
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/* ---------------------------------- */
/* save as c1i.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fi.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*50;
double a = .5;
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( (sech(x)) dx = 0.385388
(0.500
With the antiderivative of f.
F(x) = atan(sinh(x))
F(1.000) - F(0.500) = 0.385388
Press return to continue.
Calculons la primitive :
Calculer la primitive de
/ / 1
| sech(x) dx = | -------- dx
/ / cosh(x)
/ 1
= | -------- (1) dx
/ cosh(x)
/ cosh(x)
= | -------- ------- dx
/ cosh(x) cosh(x)
______________________________
/ cosh(x) | cosh**2(x) - sinh**2(x) = 1|
= | ----------- dx | |
/ cosh**2(x) | cosh**2(x) = sinh**2(x) + 1|
|____________________________|
___________________
/ 1 | u = sinh(x) |
= | --------------- cosh(x) dx | du = cosh(x) dx |
/ sinh**2(x) + 1 |_________________|
/ 1
= | ---------- du
/ u**2 + 1
= atan(u) + c
= atan(sinh(x)) + c
Remarque : (atan(u))' = 1/(u**2 + 1)
(atan(u))' = 1/(u**2 + 1)
/ /
| (atan(u))' du = | 1/(u**2 + 1) du
/ /
/
atan(u) = | 1/(u**2 + 1) du
/
/
| 1/(u**2 + 1) du = atan(u) + c
/