Mathc initiation/Fichiers c : c37cb
Installer et compiler ces fichiers dans votre répertoire de travail.
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c05b.c |
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/* ---------------------------------- */
/* save as c05b.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fb.h"
/* ---------------------------------- */
int main(void)
{
double a = 1.;
double b = 3.;
double n = 2*5.;
clrscrn();
printf(" Verify with a software that f(x) >= 0 on [%.3f,%.3f]\n\n", a, b);
printf(" f : x-> %s\n\n\n\n", feq);
stop();
clrscrn();
printf(" Draw a typical vertical rectangle on the graph.\n\n\n\n");
printf(" The length of the rectangle is : %s \n", feq);
printf(" The width of the rectangle is : dx \n\n" );
printf(" The Area of the rectangle is : (%s) * dx\n", feq);
printf(" \n\n\n\n\n");
stop();
clrscrn();
printf(" If we apply \n\n\n");
printf(" (%.3f\n", b);
printf(" int( \n");
printf(" (%.3f\n\n\n", a);
printf(" to : (%s) * dx\n\n\n", feq);
printf(" We obtain a limit of sums of areas of vertical rectangles.\n\n\n");
printf(" (%.3f\n", b);
printf(" int( (%s) * dx = %.5f\n", feq, simpson(f,a,b,n));
printf(" (%.3f\n\n\n", a);
stop();
return 0;
}
/* ---------------------------------- */
Vous trouverez ci-dessous le code Gnuplot pour dessiner la fonction et un rectangle caractèristique. Ainsi que le code pour Octave pour vérifier le calcul.
Exemple de sortie écran :
Verify with a software that f(x) >= 0 on [1.000,3.000]
f : x-> log(x)
Press return to continue.
Copier ce code dans gnuplot :
set zeroaxis lt 8
set grid
set object rect from 2.5,0 to 2.6,log(2.6)
plot [1.000:3.000] [0.000:1.200] log(x)
reset
Exemple de sortie écran :
Draw a typical vertical rectangle on the graph.
The length of the rectangle is : log(x)
The width of the rectangle is : dx
The Area of the rectangle is : (log(x)) * dx
Press return to continue.
Exemple de sortie écran :
If we apply
(3.000
int(
(1.000
to : (log(x)) * dx
We obtain a limit of sums of areas of vertical rectangles.
(3.000
int( (log(x)) * dx = 1.29582
(1.000
Press return to continue.
Vérifier le résultat avec Octave 5.2 : I = quad (f, a, b)
>> I = quad (@(x) (log(x)), 1, 3)
I = 1.2958