public class IntegralOutput {

	// =======================================================================
	// Settings for Integrations
	// =======================================================================

	// The tntegrant function.
	static final double f(double x) {
		return Math.cos(x);
	}

	static final double A = 0.0;  // The lower-limit of the integration interval.
	static final double B = 1.0;  // The upper-limit of the integration interval.
	static final int N = 10000;   // The number of tiny intervals for numerical integration.


	// =======================================================================
	// Compute The Integral Value Numerically
	// =======================================================================

	public static void main(String[] args) {
		double delta = (B - A) / N;  // The width of a tiny interval.
		double value = 0.0;  // Add approximated area of all tiny intervals to this variable.

		// Traverse tiny intervals from lower-limit (left) to upper-limit (right).
		for(int i=0; i<N; ++i) {

			// The x-coordinate value of the left-bottom point of i-th tiny interval.
			double x = A + i * delta;

			// -------------------------------------------------------------------
			// Compute area of i-th tiny interval approximately
			// (select a rule from the following), 
			// and add it to the variable "value".
			// -------------------------------------------------------------------

			// Use rectangular method (approximates area of an interval as a rectangle):
			// value += f(x) * delta;

			// Use trapezoidal method (approximates area of an interval as a trapezoid):
			// value += ( f(x) + f(x+delta) ) * delta / 2.0;

			// Use Simpson's rule (approximates f(x) in an interval as a quadratic function):
			value += ( f(x) + f(x+delta) + 4.0 * f(x+delta/2.0) ) * delta / 6.0;
		}

		// Output the computed integral value (sum of area of all tiny intervals).
		System.out.println(value);
	}
}