/* ---------------------------------- */
/* save as x_dy.h                   */
/* ---------------------------------- */
double lineintegral_dy(
double (*P_f)(double x, double y),
double (*P_g)(double t),
double (*P_h)(double t),

double a,
double b,
   int n,
   
double j  
)
{
double t;
   int i = 0;
double m = 0.;
double M = 0.;

 for(i = 0; i <= n; i++)
 {
       if(i ==0 || i== n){m = 1.;}
  else if(fmod(i,2) == 0){m = 2.;}
  else                   {m = 4.;}

  t  = (a + i*(b-a)/n);
  
           /* f(g(t),h(t)) * h(t)' */
           
  M += m * (*P_f)((*P_g)(t),(*P_h)(t)) *
  
                  fx_x((*P_h),t,j) ;
 }

  return( ((b -a)*M) / (3*n) );
}
/* ---------------------------------- */
/* ---------------------------------- */