Mathc initiation/Fichiers c : c79c02
Installer et compiler ces fichiers dans votre répertoire de travail.
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c01b.c |
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/* ---------------------------------- */
/* save as c1b.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fb.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*50;
double a = 1.;
double b = 2.;
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)
(2.000
int( (1/(1-cos(x))) dx = 1.188395
(1.000
With the antiderivative of f.
F(x) = -cot(x) - csc(x)
F(2.000) - F(1.000) = 1.188395
Press return to continue.
Calculons la primitive :
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| 1
1) Calculer la primitive de | -------- dx
| 1-cos(x)
/
/ /
| 1 | 1 1+cos(x)
| -------- dx = | -------- -------- dx
| 1-cos(x) | 1-cos(x) 1+cos(x)
/ /
/
| 1+cos(x)
= | ------------ dx
| 1-cos(x)**2
/
cos(x)**2+sin(x)**2 = 1
/
| 1+cos(x)
= | --------- dx
| sin(x)**2
/
/ /
| 1 | cos(x)
= | --------- dx + | --------- dx
| sin(x)**2 | sin(x)**2
/ /
/ /
= | csc(x)**2 dx + | cot(x) csc(x) dx
/ /
/
| 1/(1-cos(x)) dx = (-) cot(x) (-) csc(x) + c
/