

#include 

using namespace std;

//We first define two simple functions for testing with our integrator: 
//    f1(x) = x^2
double function1(double x) {
        return x*x;
}

//and f2(x) = x
double function2(double x) {
        return x;
}

//This is our function which accepts another function as an argument.  Note 
//the syntax of the first argument, in particular.
//Note also this uses the simple left endpoint approximation to the integral.
double integral( double function_to_use(double), double x_l, double x_r, int nsteps) {
        double step_size = (x_r - x_l) / double(nsteps);
        double running_sum = 0;
        for (int i = 0; i < nsteps - 1; ++i) {
                double this_x = x_l + step_size * double(i);
                double this_value = function_to_use(this_x) * step_size;
                running_sum += this_value;
        }
        return running_sum;
}

main() {
        int nsteps;
        cout << "Choose nsteps: ";
        cin >> nsteps;

        //The first call to integral uses function1, x^2, as the argument.
        double this_integral = integral(function1,-1,1,nsteps);
        double true_integral = 2./3.;
        cout << "Integral of x^2 from -1 to 1 is: ";
        cout << this_integral << endl;
        cout << "This corresponds to an error of: " << this_integral - true_integral << endl;

        //The second uses function2, x
        this_integral = integral(function2,-1,1,nsteps);
        true_integral = 0.;
        cout << "Integral of x from -1 to 1 is: ";
        cout << this_integral << endl;
        cout << "This corresponds to an error of: " << this_integral - true_integral << endl;
}