Mathc initiation/Fichiers c : c42ca
La méthode des disques, est une méthode de calcul du volume d'un solide de révolution par intégration selon un axe «parallèle» à l'axe de révolution. [wikipedia]
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c05a.c |
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/* ---------------------------------- */
/* save as c05a.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fa.h"
/* ---------------------------------- */
int main(void)
{
int n = 2*10;
double a = -1.;
double b = 1.;
clrscrn();
printf(" Compute the volume V of the solid of revolution \n");
printf(" generated by revolving R about the x-axis \n\n");
printf(" Draw the region R bounded by the graph of f, the x-axis,\n");
printf(" and the vertical lines x = a and x = b \n\n");
printf(" Let f be continous on [%.3f,%.3f].\n\n", a, b);
printf(" f : x-> %s\n\n", feq);
stop();
clrscrn();
printf(" Draw a typical vertical rectangle. \n\n");
printf(" The radius of the disk : %s \n", feq);
printf(" The thickness of the disk : dx\n");
printf(" The volume of the disk : Pi (%s)**2 dx \n\n\n", feq);
printf(" Volume of a Circular disk = Pi (radius)**2 (thickness)\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 : Pi (%s)**2 dx\n\n\n", feq);
printf(" We obtain a limit of sums of volumes of disks.\n\n\n");
printf(" (%.3f\n", b);
printf(" int( Pi (%s)**2 dx = %.3f\n", feq, simpson(VCircularDisk,a,b,n));
printf(" (%.3f\n", a);
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Exemple de sortie écran :
Compute the volume V of the solid of revolution
generated by revolving R about the x-axis
Draw the region R bounded by the graph of f, the x-axis,
and the vertical lines x = a and x = b
Let f be continous on [-1.000,1.000].
f : x-> x**2 + 2.
Press return to continue.
Dessinons avec gnuplot la fonction f :
set zeroaxis lt 8
set grid
plot [-1.000:1.000] [-3:3.000] x**2 + 2.
reset
Exemple de sortie écran :
Draw a typical vertical rectangle.
The radius of the disk : x**2 + 2.
The thickness of the disk : dx
The volume of the disk : Pi (x**2 + 2.)**2 dx
Volume of a Circular disk = Pi (radius)**2 (thickness)
Press return to continue.
Dessinons un rectangle pour construire l'équation du volume:
set zeroaxis lt 8
set grid
set object 3 rect from 0.5,0 to 0.52,0.52**2 + 2.
plot [-1.000:1.000] [-3:3.000] x**2 + 2.,\
-(x**2 + 2.)
reset
Exemple de sortie écran :
If we apply
(1.000
int(
(-1.000
to : Pi (x**2 + 2.)**2 dx
We obtain a limit of sums of volumes of disks.
(1.000
int( Pi (x**2 + 2.)**2 dx = 34.767
(-1.000
Press return to continue.
Vérifier le résultat avec Octave 5.2 : I = quad (f, a, b)
>> I = quad (@(x) pi*((x**2 + 2).*(x**2 + 2.)),-1,1)
I = 34.767