Mathc initiation/Fichiers c : c79c03
Installer et compiler ces fichiers dans votre répertoire de travail.
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c01c.c |
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/* ---------------------------------- */
/* save as c1c.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fc.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( (1/(sin(x)-1)) dx = -1.722427
(0.500
With the antiderivative of f.
F(x) = -tan(x) - sec(x)
F(1.000) - F(0.500) = -1.722427
Press return to continue.
Calculons la primitive :
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| 1
1) Calculer la primitive de | -------- dx
| sin(x)-1
/
/ /
| 1 | 1 sin(x)+1
| -------- dx = | -------- -------- dx
| sin(x)-1 | sin(x)-1 sin(x)+1
/ /
/
| sin(x)+1
= | ------------ dx
| sin(x)**2-1
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sin(x)**2+cos(x)**2 = 1
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| sin(x)+1
= | ------------- dx
| (-) cos(x)**2
/
/ /
| 1 | sin(x)
= | ------------- dx + | ------------ dx
| (-) cos(x)**2 | (-) cos(x)**2
/ /
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= (-) | sec(x)**2 dx (-) | tan(x) sec(x) dx
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| 1/(1-sin(x)) dx = (-) tan(x) (-) sec(x) + c
/