double integral using c, but deviate what I expect, please help

[Afsshl]

Dear gnu g++:

 

  I like to solve couble integral on a circle

 

 

 

 

 

I simplify it , then get

 

 

 

 

 

(not 100% sure, but almost)

 

 

so I try to ckeck it by numerical way (computer software programming)

 

the following is my simple c program to get area under curve by accumulate trapzoides

 

 

 

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#include <stdio.h>
int main() {
  int i, j;
  double  step,  sum, x[10001], z[10001];

 

  i=0; j=0; sum=0.0;

 

  step = 6.0/10000.0;
   x[0]=z[0]=-3.0;
 
   for (i=0; i<10000; i++)
       x[i+1]=z[i+1]=x[i]+step;

 

 

 

  for (i=0; i<10000; i++)
&nbs, x[10001], z[10001];

 

  i=0; j=0; sum=0.0;

 

  step = 6.0/10000.0;
   x[0]=z[0]=-3.0;
 
   for (i=0; i<10000; i++)
       x[i+1]=z[i+1]=x[i]+step;

 

 

 

  for (i=0; i<10000; i++)
    for (j=0;  j<10000; j++)
     
       if ((x[i]*x[i]+z[j]*z[j])  < 9.0)
        sum = sum +  ((9.0*x[i+1]*x[i+1]-3.0*z[j+1])+(9.0*x[i]*x[i]-3.0*z[j]))* step * 0.5;

 

  printf("sum = %f\n", sum);
}
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tested in my gcc 3.3.3 cygwin xp

$ ./a.exe
sum = 954212.727469

 

-------  which is not what I expected

 

  like to see any advice

eric