# include <cstdlib>
# include <cmath>
# include <iostream>

using namespace std;

int main ( )
//
//  INTEGRAL estimates the integral of x*x+2*x-3, from -4 to 5,
//  using random sampling.
//
//  The user enters the number of sample points to use.
//
{
  int i, n;
  double a = - 4.0, b = 5.0, error, estimate, x;
  double f ( double x );
  double random_double_ab ( double a, double b );
  double sum = 0.0;

  cout << "Enter number of points n for integral estimate: ";
  cin >> n;
//
//  This call to srand() will scramble the random number generator
//  for us.
//
  srand ( time ( ) );

  for ( i = 1; i <= n; i++ )
  {
    x = random_double_ab ( a, b );
    sum = sum + f ( x );
  }
  estimate = ( b - a ) * sum / ( double ) n;
  error = fabs ( estimate - 45.0 );
  cout << "Integral estimate using " << n << " points is "
       << estimate << "\n";
  cout << "Error is " << error << "\n";

  return 0;
}
double f ( double x )
{
  double value;
  value = x * x + 2 * x - 3;
  return value;
}
double random_double_ab ( double a, double b )
{
  double r;
  double value;
  r = ( double ) rand ( ) / ( double ) RAND_MAX;
  value = a + ( b - a ) * r;
  return value;
}