// This appears in Core Web Programming from
// Prentice Hall Publishers, and may be freely used
// or adapted. 1997 Marty Hall, hall@apl.jhu.edu.

/** A class to calculate summations and numeric
 *  integrals. The integral is calculated using
 *  the simple midpoint rule.
 */

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