/** An interface to provide a common method for executing
  * integration methods. **/
public interface Integrator
{
   public double integrate (double lo, double hi,
                           int n, Function fg);
}

/** Executes the rectangle slice method for
  * function integration. **/
class RectInteg implements Integrator
{
  public double integrate (double lo, double hi,
                            int n, Function f) {
    // Check data.
    if (hi <= lo || n <= 0 || f == null) return 0.0;
    double dx = (hi-lo)/n;
    double area = 0.0;

    double x_lo = lo;
    double x_hi = lo + dx;

    for (int i=0; i < n; i++) {
      double left_side = f.valueAt (x_lo);
      area += left_side * dx;
      x_lo = lo + i * dx;
    }

    return area;
  } // integrate

} // RectInteg

/** Executes the trapezoid method for function integration. **/
class TrapezoidInteg implements Integrator
{
  /** Integrate the 1-D function between lo and hi with n slices. */
  public double integrate (double lo, double hi,
                            int n, Function f) {
    // Check data.
    if (hi <= lo || n <= 0 || f == null) return 0.0;

    double dx =  (hi-lo)/n;
    double area = 0.0;

    double x_lo = lo;
    double x_hi = lo + dx;

    for (int i=0; i < n; i++) {
      double left_side = f.valueAt (x_lo);
      double rite_side = f.valueAt (x_hi);
      area += dx * (left_side + rite_side) / 2.0;
      x_lo = lo + i*dx;
      x_hi = x_lo + dx;
    }

    return area;
  } // integrate

} // TrapezoidInteg

import java.applet.*;

/** This class illustrates use of Rectangular and Trapezoidal
  * methods for integration.
  *
  *  Integrator.java - interface
  *  TravezoidInteg.java - implements Integrator
  *  RectInteg.java  - implements Integrator
  *
  *  Function.java - interface
  *  PolyFunc.class - see below
 **/
public class IntegrateApplet extends Applet
{
  public void init () {

     PolyFunc pf = new PolyFunc ();

     RectInteg ri = new RectInteg ();
     double integ = ri.integrate (-2.0,2.0,100,pf);
     System.out.println ("Rectangle integ = "+ integ);

     TrapezoidInteg ti = new TrapezoidInteg ();
     integ = ti.integrate (-2.0,2.0,100,pf);
     System.out.println ("Trapezoid integ = " + integ);

  } // init

  /** Paint message in Applet window. **/
  public void paint (java.awt.Graphics g) {
     g.drawString ("IntegrateApplet",20,20);
  }

  /** This program can also run as an application. No graphics
    * needed, so it just runs the applet's init () function.
   **/
  public static void main (String [] args) {
    IntegrateApplet obj = new IntegrateApplet ();
    obj.init ();
  } // main

} // IntegrateApplet

/** Implement a simple second order polynomial. **/
class PolyFunc implements Function
{
   public double valueAt (double x) {
     return  (4.0 - x*x);
   }

} // Function