Mathc initiation/Fichiers c : c72c02
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 = 0.;
double b = 3.;
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)
(3.000
int( ((x+6) / (x+5)**(1/2)) dx = 8.816103
(0.000
With the antiderivative of f.
F(x) = (2/3) pow((x+5),3/2) + (2) pow((x+5),1/2)
F(3.000) - F(0.000) = 8.816103
Press return to continue.
Calculons la primitive :
Calculer la primitive de
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| (x+6) / sqrt(x+5) dx =
/
________________ ___________________
| u = (x+5) | | x = u-5 |
| du = dx | | (x+6) = (u-5) + 6 |
|_______________| | |
| (x+6) = u + 1 | | (x+6) = u + 1 |
|_______________| |___________________|
/ /
| (x+6) / sqrt(x+5) dx = | (u+1) / sqrt(u) du
/ /
/
= | (u+1) / u**(1/2) du
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= | (u+1) * u**(-1/2) du
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= | (u**(1/2) + u**(-1/2)) du
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= (2/3) u**(3/2) + (2) u**(1/2)) + c
/
| (x+6) / sqrt(x+5) dx = (2/3) (x+5)**(3/2) + (2) (x+5)**(1/2)) + c
/