Example 3: Integral of the entire real line
The integral is computed and compared to its expected value. This integral is evaluated in Gradshteyn and Ryzhik (equation 3.417.1).
import com.imsl.math.*;
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);
}
}
Output
result = 0.10615051707662819
expect = 0.10615051707663337
Link to Java source.
Reference
Gradshteyn, I. S. and I. M. Ryzhik (1965), Table of Integrals, Series, and Products
, Academic Press, New York.