package com.imsl.test.example.math;

import com.imsl.math.*;

/**
 * <p>
 * Quadrature Example 3: Approximates the integral of the entire real line.</p>
 *
 * The integral $$\int_{-\infty}^\infty \frac{x} {4e^x + 9e^{-x}} \, dx$$ is
 * computed and compared to its expected value. This integral is evaluated in
 * Gradshteyn and Ryzhik (equation 3.417.1).
 *
 * @see <a href="QuadratureEx3.java">Code</a>
 * @see <a href="doc-files/QuadratureEx3.out">Output</a>
 */
public class QuadratureEx3 {

    public static void main(String args[]) {
        Quadrature.Function fcn = new Quadrature.Function() {
            public double f(double x) {
                return x / (4 * Math.exp(x) + 9 * Math.exp(-x));
            }
        };

        Quadrature q = new Quadrature();
        double result = q.eval(fcn, Double.NEGATIVE_INFINITY,
                Double.POSITIVE_INFINITY);

        double expect = Math.PI * Math.log(1.5) / 12.;
        System.out.println("result = " + result);
        System.out.println("expect = " + expect);
    }
}