Mathc initiation/001T

Sommaire

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	c00b.c

/* --------------------------------- */
/* save as c00b.c                    */
/* --------------------------------- */
#include  "x_hfile.h"
#include       "fb.h"
/* --------------------------------- */
int main(void)
{
double  M =     simpson(f,a, b, LOOP);
double  N =     simpson(g,a, b, LOOP);
double  P =     simpson(h,a, b, LOOP);                          

 clrscrn();
 printf("Second property of linearity,              \n\n" 
 
        "   (b                 (b            (b       \n"
        "int(g(x)+h(x) dx = int(g(x) dx + int(h(x) dx \n"
        "   (a                 (a            (a   \n\n\n");
        
 printf(" g  : (x)-> %s          \n",  geq);
 printf(" h  : (x)-> %s        \n\n",  heq);
 
 printf(" f  : (x)-> %s        \n\n",  feq);
 printf("     f(x) =  g(x) + h(x) \n\n");
 stop();
  
 clrscrn();  
 printf(" f  : (x)-> %s          \n\n",  feq);
    
 printf("         (%.3f            \n", b);
 printf(" M =  int(  %s  dx = %.6f \n", feq, M);
 printf("         (%.3f        \n\n\n", a);

 printf(" g  : (x)-> %s                 \n\n", geq);
 
 printf("        (%.3f            \n", b);
 printf(" N = int(  %s  dx = %.6f \n", geq,  N);
 printf("        (%.3f        \n\n\n", a);
 
 
 printf(" h  : (x)-> %s          \n\n", heq);
 
 printf("        (%.3f             \n", b);
 printf(" P = int(   %s  dx = %.6f \n", heq, P);
 printf("        (%.3f         \n\n\n", a);
 stop();

 clrscrn();
 printf("Second property of linearity            \n\n" 

        "          (b                              \n"
        " M   = int( g(x) + h(x) dx         = %.6f \n"
        "          (a                            \n\n"

        "          (b             (b               \n"
        " N+P = int( g(x) dx + int( h(x) dx = %.6f \n"
        "          (a             (a           \n\n\n",                
        M, N+P);
  stop();

 return 0;
}
/* --------------------------------- */
/* --------------------------------- */

Verifier avec mathematica : Free: wolframalpha.com

integral (x**2 + cos(x)+1)  dx from 0 to 1

Exemple de sortie écran :

Second property of linearity,              

   (b                 (b            (b       
int(g(x)+h(x) dx = int(g(x) dx + int(h(x) dx 
   (a                 (a            (a   


 g  : (x)-> (x**2)          
 h  : (x)-> (cos(x)+1)        

 f  : (x)-> (x**2)+(cos(x)+1)        

     f(x) =  g(x) + h(x) 

 Press return to continue. 


 f  : (x)-> (x**2)+(cos(x)+1)          

         (1.000            
 M =  int(  (x**2)+(cos(x)+1)  dx = 2.174804 
         (0.000        


 g  : (x)-> (x**2)                 

        (1.000            
 N = int(  (x**2)  dx = 0.333333 
        (0.000        


 h  : (x)-> (cos(x)+1)          

        (1.000             
 P = int(   (cos(x)+1)  dx = 1.841471 
        (0.000         


 Press return to continue. 


Second property of linearity            

          (b                              
 M   = int( g(x) + h(x) dx         = 2.174804 
          (a                            

          (b             (b               
 N+P = int( g(x) dx + int( h(x) dx = 2.174804 
          (a             (a           


 Press return to continue.