Mathc initiation/Fichiers c : c72c02


Sommaire


Installer et compiler ces fichiers dans votre répertoire de travail.

c01b.c
/* ---------------------------------- */
/* save as c1b.c                      */
/* ---------------------------------- */
#include "x_hfile.h"
#include      "fb.h"
/* ---------------------------------- */
int main(void)
{
int      n =  2*50;
double   a =  0.;
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+6) / (x+5)**(1/2))  dx = 8.816103
    (0.000



 With the antiderivative of f.

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


 F(3.000) -  F(0.000)  = 8.816103 


 Press return to continue.



Calculons la primitive :
                           
Calculer la primitive de 
                                 
       
        /               
       | (x+6) / sqrt(x+5)  dx = 
       /               

                         ________________            ___________________ 
                        |     u = (x+5) |           |     x =  u-5      |
                        |    du =   dx  |           | (x+6) = (u-5) + 6 |           
                        |_______________|           |                   |
                        | (x+6) = u + 1 |           | (x+6) =  u    + 1 |
                        |_______________|           |___________________|
     
     
        /                          /
       | (x+6) / sqrt(x+5)  dx =  | (u+1) / sqrt(u) du
       /                          /
            

                                    /
                                =  | (u+1) / u**(1/2) du
                                   /
                                   

                                    /
                                =  | (u+1) * u**(-1/2) du
                                   /
                                   
                                    /
                                =  | (u**(1/2) + u**(-1/2)) du
                                   /                                                               
                                           
                                =  (2/3) u**(3/2) + (2) u**(1/2)) + c                                 
                                               
        /                         
       | (x+6) / sqrt(x+5)  dx =  (2/3) (x+5)**(3/2) + (2) (x+5)**(1/2)) + c
       /