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