# include "quad_serial.hpp"

using namespace std;

//****************************************************************************80

double quad_serial ( double f ( double x ), double a, double b, int n )

//****************************************************************************80
//
//  Purpose:
//
//    quad_serial() estimates the integral of a function.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    18 October 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    function f ( x ): the function whose integral is to be estimated.
//
//    real a, b: the limits of integration.
//
//    integer n: the number of 
//
//  Output:
//
//    real q: an estimate for the integral of f(x) over the interval.
//
{
  int i;
  double q;
  double x;

  q = 0.0;
  for ( i = 0; i < n; i++ )
  {
    x = ( ( n - i - 1 ) * a + ( i ) * b ) / ( n - 1 );
    q = q + f ( x );
  }

  q = ( b - a ) * q / ( double ) n;

  return q;
}