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#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <conio.h>
#include <iostream.h>


void main()
  {
     clrscr();
     cout<<"\n                 Welcome!\n\n";
     cout<<"I = x*sin(x)/(1 + x^2),  [0,1]\n\n";
     double a,b,I;
     float a1,b1;
     double F(double);
     double GAUS(double,double);
     printf("Input a: ");
     scanf("%f",&a1);
     a = a1;
     printf("Input b: ");
     scanf("%f",&b1);
     b = b1;
     I = GAUS(a,b);
     printf("\nMethod of Gauss:  I = %f",I);
     cout<<"\n\nPress any key to exit, please.\n";
     getch();
  }


double F(double x)
   {
     double s;
     s = (x*sin(x)/(1+x*x));
     return (s);
   }

double GAUS(double L,double R)
   {
     float X5,X6,X7,X8,A5,A6,A7,A8;
     float A1=A8=0.10122854,
	   A2=A7=0.22238103,
	   A3=A6=0.31370664,
	   A4=A5=0.36268378;
     float X1=-0.96028986,
	   X2=-0.79666648,
	   X3=-0.52553242,
	   X4=-0.18343464;
	   X5=-X4;
	   X6=-X3;
	   X7=-X2;
	   X8=-X1;

     float s=(R-L)/2*(A1*F((L+R)/2+(R-L)/2*X1)+A2*F((L+R)/2+(R-L)/2*X2)+A3*F((L+R)/2+(R-L)/2*X3)+A4*F((L+R)/2+(R-L)/2*X4)+A5*F((L+R)/2+(R-L)/2*X5)+A6*F((L+R)/2+(R-L)/2*X6)+A7*F((L+R)/2+(R-L)/2*X7)+A8*F((L+R)/2+(R-L)/2*X8));
     return(s);
   }
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