import java.applet.*;
import java.awt.*;


public class Example6_5 extends Applet
{
 public static double f(double x)
 {double y;
  y=Math.exp(-x*x);
  return y; }

 public static double GaussLegendre(double a,double b,int n)
  {double s;
   double[] y=new double[5];
   double[] x=new double[5];
   int i;
   if(n==0){x[0]=0;y[0]=2;}
   else if(n==1){x[0]=-0.5773502692;x[1]=0.5773502692;y[0]=y[1]=1;}
   else if(n==2){x[0]=-0.7745966692;x[1]=0;x[2]=0.7745966692;
                 y[0]=5.0/9;y[1]=8.0/9;y[2]=5.0/9;}
   else if(n==3){x[0]=-0.8611363116;x[1]=-0.3399810436;x[2]=0.3399810436;x[3]=0.8611363116;
                 y[0]=y[3]=0.3478548451;y[1]=y[2]=0.6521451549;}
   else if(n==4){x[0]=-0.9061798459;x[1]=-0.5384693101;x[2]=0;x[3]=0.5384693101;x[4]=0.9061798459;
                 y[0]=y[4]=0.2369268851;y[1]=y[3]=0.4786286705;y[2]=0.5688888889;}
   s=0;
   for(i=0;i<=n;i++)
   {s+=y[i]*f(((b-a)*x[i]+b+a)/2);}
   s*=(b-a)/2;
   return s;

}
public void paint(Graphics g)
{double y;
 int n;
 for(n=0;n<=4;n++)
 {y=GaussLegendre(1,1.5,n);
  g.drawString("I"+n+"="+y,10,20+20*n);
 }
}}