Mathc initiation/Fichiers c : c38ca
Installer et compiler ces fichiers dans votre répertoire de travail.
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c05a.c |
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/* ---------------------------------- */
/* save as c05a.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fa.h"
/* ---------------------------------- */
int main(void)
{
double a = 0.2;
double b = 0.8;
double n = 2*5.;
clrscrn();
printf(" Verify with a software that g(x) >= h(x) on [%.3f,%.3f].\n\n\n", a, b);
printf(" g : x-> %s\n\n", geq);
printf(" h : x-> %s\n\n", heq);
stop();
clrscrn();
printf(" Draw a typical vertical rectangle on a graph.\n\n");
printf(" Upper boundary (g) : %s \n",geq);
printf(" lower boundary (h) : %s \n\n",heq);
printf(" The length of the rectangle is : (%s) - (%s) \n",geq, heq);
printf(" The width of the rectangle is : dx \n\n");
printf(" The Area of the rectangle is : ((%s) - (%s)) * dx\n",geq, heq);
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) - (%s)) * dx\n\n", geq, heq);
printf(" We obtain a limit of sums of areas of vertical rectangles.\n\n\n");
printf(" (%.3f\n", b);
printf(" int( [(%s) - (%s)] dx = %.5f\n",
geq,heq,simpson(gminuh,a,b,n));
printf(" (%.3f\n\n\n", a);
stop();
return 0;
}
/* ---------------------------------- */
Vous trouverez ci-dessous le code Gnuplot pour dessiner les fonctions et un rectangle caractèristique. Ainsi que le code pour Octave pour vérifier le calcul.
Exemple de sortie écran :
Verify with a software that g(x) >= h(x) on [0.200,0.800].
g : x-> sqrt(x)
h : x-> x**2
Press return to continue.
Copier ce code dans gnuplot :
set zeroaxis lt 8
set grid
set object rect from 0.5,(0.5*0.5) to 0.52,sqrt(0.52)
plot [ 0.2:0.8] [0.000:1.000] sqrt(x), (x*x)
reset
Exemple de sortie écran :
Draw a typical vertical rectangle on a graph.
Upper boundary (g) : sqrt(x)
lower boundary (h) : x**2
The length of the rectangle is : (sqrt(x)) - (x**2)
The width of the rectangle is : dx
The Area of the rectangle is : ((sqrt(x)) - (x**2)) * dx
Press return to continue.
Exemple de sortie écran :
If we apply
(0.800
int(
(0.200
to : ((sqrt(x)) - (x**2)) * dx
We obtain a limit of sums of areas of vertical rectangles.
(0.800
int( [(sqrt(x)) - (x**2)] dx = 0.24940
(0.200
Press return to continue.
Vérifier le résultat avec Octave 5.2 : I = quad (f, a, b)
>> I = quad (@(x) (sqrt(x)-(x.*x)), 0.2,0.8)
I = 0.24940