1 /*
2  * Copyright Nick Thompson, 2017
3  * Use, modification and distribution are subject to the
4  * Boost Software License, Version 1.0. (See accompanying file
5  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
6  *
7  * This example shows to to numerically integrate a periodic function using the adaptive_trapezoidal routine provided by boost.
8  */
9 
10 #include <iostream>
11 #include <cmath>
12 #include <limits>
13 #include <boost/math/quadrature/trapezoidal.hpp>
14 
main()15 int main()
16 {
17     using boost::math::constants::two_pi;
18     using boost::math::constants::third;
19     using boost::math::quadrature::trapezoidal;
20     // This function has an analytic form for its integral over a period: 2pi/3.
21     auto f = [](double x) { return 1/(5 - 4*cos(x)); };
22 
23     double Q = trapezoidal(f, (double) 0, two_pi<double>());
24 
25     std::cout << std::setprecision(std::numeric_limits<double>::digits10);
26     std::cout << "The adaptive trapezoidal rule gives the integral of our function as " << Q << "\n";
27     std::cout << "The exact result is                                                 " << two_pi<double>()*third<double>() << "\n";
28 
29 }
30