/** A class to calculate summations and numeric integrals. The
 *  integral is calculated according to the midpoint rule.
 *
 *  Taken from Core Web Programming from 
 *  Prentice Hall and Sun Microsystems Press,
 *  http://www.corewebprogramming.com/.
 *  © 2001 Marty Hall and Larry Brown;
 *  may be freely used or adapted. 
 */

public class Integral {
  /** Returns the sum of f(x) from x=start to x=stop, where the
   *  function f is defined by the evaluate method of the 
   *  Evaluatable object.
   */

  public static double sum(double start, double stop,
                           double stepSize,
                           Evaluatable evalObj) {
    double sum = 0.0, current = start;
    while (current <= stop) {
      sum += evalObj.evaluate(current);
      current += stepSize;
    }
    return(sum);
  }

  /** Returns an approximation of the integral of f(x) from 
   *  start to stop, using the midpoint rule. The function f is
   *  defined by the evaluate method of the Evaluatable object.
   */
  
  public static double integrate(double start, double stop,
                                 int numSteps, 
                                 Evaluatable evalObj) {
    double stepSize = (stop - start) / (double)numSteps;
    start = start + stepSize / 2.0;
    return(stepSize * sum(start, stop, stepSize, evalObj));
  }
}