public class Integ{

	public static double trap(double mag, double dx, double xMax){
		double sum=0.;
		double x=0;
		int nPts=0;
		do {
			sum=sum+mag*(Math.sin(x)+Math.sin(x+dx))*dx/2.;
			nPts++;
			x+=dx;
		} while (x<xMax);

		return sum; 
	}

	public static double simp(double mag, double dx, double xMax){
		double sum=0.;
		double x=dx;
		int nPts=1;
		sum=mag*Math.sin(0.)*dx/3.;
		do {
			sum=sum+mag*(4.*Math.sin(x)+2.*Math.sin(x+dx))*dx/3.;
			nPts+=2;
			x+=2*dx;
		} while (x<xMax);
		sum-=mag*Math.sin(x-dx)*dx/3.;
		return sum; 
	}

	public static void main(String[] argv){
		System.out.println("trap");
		System.out.println("\t 0..Pi, 2 sin(x)="+trap(2.,0.1,Math.PI)); 
		System.out.println("\t 0..2Pi, 2 sin(x)="+trap(2.,0.1,2.*Math.PI)); 
		System.out.println("\t 0..Pi, 2 sin(x)="+trap(2.,0.01,Math.PI)); 
		System.out.println("\t 0..2Pi, 2 sin(x)="+trap(2.,0.01,2.*Math.PI)); 

		System.out.println("simpson");
		System.out.println("\t 0..Pi, 2 sin(x)="+simp(2.,0.1,Math.PI)); 
		System.out.println("\t 0..2Pi, 2 sin(x)="+simp(2.,0.1,2.*Math.PI)); 
		System.out.println("\t 0..Pi, 2 sin(x)="+simp(2.,0.01,Math.PI)); 
		System.out.println("\t 0..2Pi, 2 sin(x)="+simp(2.,0.01,2.*Math.PI)); 

		System.out.println("testing machine precision");
		System.out.println("\t 0..Pi, 2e15 sin(x)="+simp(2.e25,1e-3,Math.PI)); 
		System.out.println("\t 0..Pi, 2e15 sin(x)="+simp(2.e25,1e-3,2.*Math.PI)); 
		System.out.println("reducing step...");
		System.out.println("\t 0..Pi, 2e15 sin(x)="+simp(2.e25,1e-5,Math.PI)); 
		System.out.println("\t 0..Pi, 2e15 sin(x)="+simp(2.e25,1e-5,2.*Math.PI)); 
		System.out.println("reducing step...");
		System.out.println("\t 0..Pi, 2e15 sin(x)="+simp(2.e25,1e-7,Math.PI)); 
		System.out.println("\t 0..Pi, 2e15 sin(x)="+simp(2.e25,1e-7,2.*Math.PI)); 
	}

}
/*
output: 

S:\OSUsite\web-content\COURSES\ph265>java Integ
trap
         0..Pi, 2 sin(x)=3.993258505082435
         0..2Pi, 2 sin(x)=2.824915878503068E-4
         0..Pi, 2 sin(x)=3.9998959841428467
         0..2Pi, 2 sin(x)=4.643947145279121E-5
simpson
         0..Pi, 2 sin(x)=3.99659177456306
         0..2Pi, 2 sin(x)=0.006915809800260877
         0..Pi, 2 sin(x)=3.9999974636773024
         0..2Pi, 2 sin(x)=1.0146173177758311E-5
testing machine precision
         0..Pi, 2e15 sin(x)=3.999999834069056E25
         0..Pi, 2e15 sin(x)=6.6372404791309844E18
reducing step...
         0..Pi, 2e15 sin(x)=3.9999999999461964E25
         0..Pi, 2e15 sin(x)=5.460507706942569E14
reducing step...
         0..Pi, 2e15 sin(x)=4.0000000002982025E25
         0..Pi, 2e15 sin(x)=-4.7109021685244376E16

*/