Mathc initiation/Fichiers c : c74c03
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 = 0.;
double b = .5;
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)
(0.500
int( (tan(x)) dx = 0.130584
(0.000
With the antiderivative of f.
F(x) = - ln( |cos(x)| )
F(0.500) - F(0.000) = 0.130584
Press return to continue.
Calculons la primitive :
Calculer la primitive de
/ /
| tan(x) dx = | sin(x)/cos(x) dx
/ /
___________________________
/ sin(x) dx | u = cos(x) |
= | ----- | du = (-1) sin(x) dx |
/ cos(x) |(-1) du = sin(x) dx |
|_________________________|
/ / (-1) du
| tan(x) dx = | -----
/ / u
/ / 1
| tan(x) dx = (-1) | ----- du
/ / u
= - ln( |u| ) + c
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= - ln( |cos(x)| ) + c | (-1) ln(a ) = ln( 1/a) |
| (-1) ln(|cos(x)|) = ln( |1/cos(x)|) |
= ln( |sec| ) + c | = ln( |sec(x)|) |
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