Mathc initiation/Fichiers c : c72c04


Sommaire


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c01d.c
/* ---------------------------------- */
/* save as c1d.c                      */
/* ---------------------------------- */
#include "x_hfile.h"
#include      "fd.h"
/* ---------------------------------- */
int main(void)
{
int      n =  2*50;
double   a =  2.;
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/sqrt(2*x-1))  dx = 4.997493
    (2.000



 With the antiderivative of f.

 F(x) = 2/3 (2*x-1)**(3/2) + 2 (2*x-1)**(1/2) 


 F(3.000) -  F(2.000)  = 4.997493 


 Press return to continue.



Calculons la primitive :
                           
Calculer la primitive de 
                                 
       
        / 
       |      4x           
       |   ----------  dx = 
       |   sqrt(2x-1)          
       /               
                        __________________            _____________
                        |      u = (2x-1) |          | u = (2x-1)  |    
                        |     du =  2 dx  |          |             | 
                        | 1/2 du =    dx  |          | x = (u+1)/2 |         
                        |_________________|          |_____________|
     
        / 
       |   4(u+1)/2           
       |   --------  1/2 du = 
       |   sqrt(u)          
       /             
             
                            
        / 
       |    (u+1)           
       |   -------   du = 
       |   sqrt(u)          
       /             
 
 
        /                   / 
       |     u             |     1 
       |   -------   du +  |   -------   du =
       |   u**(1/2)        |   u**(1/2)
       /                   / 
       
       
        /                   / 
       |  u**(1/2)   du +  |   u**(-1/2) du =
       /                   /        
       
       
       
        / 
       |      4x           
       |   ----------  dx =  2/3 u**(3/2) + 2 u**(1/2)
       |   sqrt(2x-1)          
       /             
       
                          =  2/3 (2x-1)**(3/2) + 2 (2x-1)**(1/2)