// TrapezoidAbs.java

// Use abstract methods to use the trapezoid rule to approximate the
// integral of an arbitrary function.


// Use the trapezoid rule to approximate the integral of f from A to B
// using N trapezoids.

abstract class Trapezoid {

  public abstract double f(double x);

  public double ComputeTrapezoid(double A, double B, int N) {
     if ((B < A) || N < 2) return 0.0;
     double Delta = (B-A)/N;
     double Sum = (f(B)+f(A))/2;
     for (int i=1; i<N; i++) Sum = Sum + f(A + i*Delta);
     return Delta * Sum;
  }

}  // end Trapezoid

// TrapezoidSquare applies the Trapezoid rule to f(x) = x^2;

class TrapezoidSquare extends Trapezoid {

   public double f(double x) { return x*x; }

} // end TrapezoidSquare

// TrapezoidW applies the trapezoid ruld to f(x) = 1/(1+x^2)

class TrapezoidW extends Trapezoid {

   public double f(double x) { return 1/(1+x*x); }

} // end TrapezoidW

// TrapezoidAbs computes the integral of x^2 from 0.0 to 3.0, and the 
// integral of 1/1+x^2 from 0.0 to 1.0.


public class TrapezoidAbs {
public static void main(String args[]) {
TrapezoidSquare TS = new TrapezoidSquare();
System.out.println(TS.ComputeTrapezoid(0.0, 3.0, 101));
TrapezoidW TW = new TrapezoidW();
System.out.println(TW.ComputeTrapezoid(0.0, 1.0, 101));

}


} // end TrapezoidAbs