Mathc initiation/Fichiers c : c72c03


Sommaire


Installer et compiler ces fichiers dans votre répertoire de travail.

c01c.c
/* ---------------------------------- */
/* save as c1c.c                      */
/* ---------------------------------- */
#include "x_hfile.h"
#include      "fc.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(      ((x**3) * (x**2+5)**(1/2))  dx = 66.226202
    (1.000



 With the antiderivative of f.

 F(x) = (1/5)*pow((pow(x,2)+5),5/2) - (5/3)*pow((pow(x,2)+5),3/2) 


 F(3.000) -  F(1.000)  = 66.226202 


 Press return to continue.



Calculons la primitive :
                           
Calculer la primitive de 
                                 
       
        /               
       | x**3 * sqrt(x**2+5)  dx = 
       /               
                        _____________________            _________________
                        |      u = (x**2+5) |           |    u = (x**2+5) |
                        |     du = 2*x dx   |           |                 |               
                        | 1/2 du =   x dx   |           | x**2 = (u-5)    |
                        |___________________|           |_________________|
     
     
        /                          /
       | x**3  sqrt(x**2+5) dx =  | x**2  (x**2+5)**(1/2)   x dx 
       /                          /
            
                                    /
                                =  | (u-5) u**(1/2)      (1/2)du
                                   /
                                   
                                          /
                                =  (1/2) | (u-5) u**(1/2) du
                                         /
                                        
                                          /
                                =  (1/2) | (u**(3/2) - (5)u**(1/2))  du
                                         /
                                                                                  
                                =   (1/2)(2/5) (u**(5/2) - (1/2)(2/3) (5)u**(3/2)) + c
                                
                                =   (1/5) u**(5/2) - (5/3) u**(3/2) + c                                
                                                                                  
                                                       
        /                         
       | (x+6) * sqrt(x+5)  dx =  (1/5) (x**2+5)**(5/2) - (5/3) (x**2+5)**(3/2)) + c
       /