Mathc initiation/Fichiers c : c72c04
Installer et compiler ces fichiers dans votre répertoire de travail.
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c01d.c |
|---|
/* ---------------------------------- */
/* save as c1d.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fd.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*50;
double a = 2.;
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( (4*x/sqrt(2*x-1)) dx = 4.997493
(2.000
With the antiderivative of f.
F(x) = 2/3 (2*x-1)**(3/2) + 2 (2*x-1)**(1/2)
F(3.000) - F(2.000) = 4.997493
Press return to continue.
Calculons la primitive :
Calculer la primitive de
/
| 4x
| ---------- dx =
| sqrt(2x-1)
/
__________________ _____________
| u = (2x-1) | | u = (2x-1) |
| du = 2 dx | | |
| 1/2 du = dx | | x = (u+1)/2 |
|_________________| |_____________|
/
| 4(u+1)/2
| -------- 1/2 du =
| sqrt(u)
/
/
| (u+1)
| ------- du =
| sqrt(u)
/
/ /
| u | 1
| ------- du + | ------- du =
| u**(1/2) | u**(1/2)
/ /
/ /
| u**(1/2) du + | u**(-1/2) du =
/ /
/
| 4x
| ---------- dx = 2/3 u**(3/2) + 2 u**(1/2)
| sqrt(2x-1)
/
= 2/3 (2x-1)**(3/2) + 2 (2x-1)**(1/2)