Mathc initiation/001N

Sommaire

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	c00b.c

/* --------------------------------- */
/* save as c00b.c                    */
/* --------------------------------- */
#include  "x_hfile.h"
#include       "fb.h"
/* --------------------------------- */
int main(void)
{
double M = simpson_dydx(f, ay,by,LOOP, ax,bx,LOOP);
double N = simpson_dydx(g, ay,by,LOOP, ax,bx,LOOP);
double P = simpson_dydx(h, ay,by,LOOP, ax,bx,LOOP);

 clrscrn();
 printf("Second property of linearity                            \n\n" 
 
"    (b (d                       (b (d              (b (d          \n"
" int( g(x,y) + h(x,y) dydx = int( g(x,y) dydx + int( h(x,y) dydx  \n"
"    (a (c                       (a (c              (a (c      \n\n\n");
        
 stop();
 
 clrscrn();   
 printf(" g  : (x,y)-> %s             \n",  geq);
 printf(" h  : (x,y)-> %s           \n\n",  heq);
 
 printf(" f  : (x,y)-> %s           \n\n",  feq);
 printf(" f(x,y) =  g(x,y) + h(x,y) \n\n");
 stop();
 
 clrscrn();  
 printf(" f  : (x,y)-> %s           \n\n",  feq);
    
 printf("         (%.3f  (%s               \n", bx,byeq);
 printf(" M =  int(    int( %s  dydx = %.6f\n", feq, M);
 printf("         (%.3f  (%s           \n\n\n", ax,ayeq);

 printf(" g  : (x,y)-> %s                  \n\n", geq);
 
 printf("        (%.3f  (%s                  \n", bx,byeq);
 printf(" N = int(    int(  %s  dydx = %.6f  \n", geq,  N);
 printf("        (%.3f  (%s              \n\n\n", ax,ayeq);
 
 
 printf(" h  : (x,y)-> %s                  \n\n", heq);
 
 printf("        (%.3f  (%s                  \n", bx,byeq);
 printf(" P = int(    int(  %s  dydx = %.6f  \n", heq, P);
 printf("        (%.3f  (%s              \n\n\n", ax,ayeq);
 stop();
 
 clrscrn();
 printf("Second property of linearity                    \n\n" 
 
        "          (b (d                                   \n"
        " M   = int( g(x,y) + h(x,y) dydx           = %.6f \n"
        "          (a (c                                 \n\n"

        "          (b (d              (b (d                \n"
        " N+P = int( g(x,y) dydx + int( h(x,y) dydx = %.6f \n"
        "          (a (c              (a (c            \n\n\n",                
        M, N+P);
        
 stop();
 
 return 0;
}

Verifier avec mathematica : Free: wolframalpha.com

 integral (x*y + 2*y**2*x+1) dydx from 0 to 1 from 0 to (2-2*x)

Exemple de sortie écran :

Second property of linearity                            

    (b (d                       (b (d              (b (d          
 int( g(x,y) + h(x,y) dydx = int( g(x,y) dydx + int( h(x,y) dydx  
    (a (c                       (a (c              (a (c      


 Press return to continue. 


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

 f  : (x,y)-> x*y + 2*y**2*x+1           

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

 Press return to continue. 


 f  : (x,y)-> x*y + 2*y**2*x+1           

         (1.000  (2-2*x               
 M =  int(    int( x*y + 2*y**2*x+1  dydx = 1.433333
         (0.000  (0           


 g  : (x,y)-> x*y                  

        (1.000  (2-2*x                  
 N = int(    int(  x*y  dydx = 0.166667  
        (0.000  (0              


 h  : (x,y)-> 2*y**2*x+1                  

        (1.000  (2-2*x                  
 P = int(    int(  2*y**2*x+1  dydx = 1.266667  
        (0.000  (0              


 Press return to continue. 


Second property of linearity                    

          (b (d                                   
 M   = int( g(x,y) + h(x,y) dydx           = 1.433333 
          (a (c                                 

          (b (d              (b (d                
 N+P = int( g(x,y) dydx + int( h(x,y) dydx = 1.433333 
          (a (c              (a (c            


 Press return to continue.