Mathc initiation/Fichiers c : c72c11
Installer et compiler ces fichiers dans votre répertoire de travail.
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c01i.c |
|---|
/* ---------------------------------- */
/* save as c1i.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fi.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*50;
double a = 1.;
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+5)/(1+(4*x+5)**2)) dx = 0.157895
(1.000
With the antiderivative of f.
F(x) = 1/8*ln(|1+(4*x+5)**2|)
F(3.000) - F(1.000) = 0.157895
Press return to continue.
Calculons la primitive :
Calculer la primitive de
/ (4x+5)
| ----------- dx =
/ 1+(4x+5)**2
_________________________
| u = 1+(4x+5)**2 |
| du =(2)(4x+5)(4) dx |
|1/8 du = (4x+5) dx |
|_________________________|
/ 1
| ----------- (4x+5) dx =
/ 1+(4x+5)**2
1 / 1
--- | --- du = 1/8 ln(u) + c
8 / u
= 1/8 ln(1+(4x+5)**2) + c
Remarque 1 :
/ (4x+8)
| ----------- dx =
/ 1+(4x+5)**2
/ (4x+5) / 3
| ----------- dx + | ----------- dx
/ 1+(4x+5)**2 / 1+(4x+5)**2
__________________
| u = 4x+5 |
| du = 4 dx |
|1/4 du = dx |
|__________________|
/ (4x+5) 3 / 1
| ----------- dx + --- | -------- du
/ 1+(4x+5)**2 4 / 1 + u**2
= 1/8 ln(1+(4x+5)**2) + 3/4 atan(u) + c
= 1/8 ln(1+(4x+5)**2) + 3/4 atan(4x+5) + c
Remarque 2 :
/ (4x+5)**2
| ----------- dx =
/ 1+(4x+5)**3
____________________________
| u = 1+(4x+5)**3 |
| du =(3)(4x+5)**2(4) dx |
|1/12 du = (4x+5)**2 dx |
|____________________________|
/ 1
| ----------- (4x+5)**2 dx =
/ 1+(4x+5)**3
1 / 1
---- | --- du = 1/12 ln(u) + c
12 / u
= 1/12 ln(1+(4x+5)**3) + c
Remarque 3 :
/ (4x+5)**(-1/2)
| --------------- dx =
/ 1+(4x+5)**(1/2)
_____________________________________
| u = 1+(4x+5)**(1/2) |
| du = (1/2)(4x+5)**(-1/2)(4) dx |
|(1/2) du = (4x+5)**(-1/2) dx |
|_____________________________________|
/ 1
| ----------------- (4x+5)**(-1/2) dx =
/ 1+(4x+5)**(1/2)
1 / 1
--- | --- du = 1/2 ln(u) + c
2 / u
= 1/2 ln(1+(4x+5)**(1/2)) + c =
...