Integrating Functions w/ Simpson's Rule:

[Bennigan88]

Hey guys, my first post so forgive me if I balls up posting this code. Anyway, this is my program for calculating the indefinite integral of any programmer-defined function given two limits of integration. Any thoughts or comments would be appreciated!

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

    using namespace std;


    bool even(int x) //simple even test. if even, returns 1
    {
        if (x%2==0)
            return 1;
        else
            return 0;
    }
    double f(double x) //here function of curve is defined by programmer
    {
        //here programmer defines function of curve
        //const long double e = 2.718281828459045235360287471352662497757247093;
        return (pow(x,3));


    }
    int choose_coef(int i, int n) //these coefficients are based on Simpon's Rule
    {
        if (i==0 || i==n) //first and last time around
            return 1;
        else if (!(even(i))) //if i is odd
            return 4;
        else
            return 2;
    }

    int main()
    {

        double a=0;
        double b=0;
        int p=0;
        int n=0;
        double dx=0;
        char ans;

        cout.setf(ios::fixed);
        cout.setf(ios::showpoint);
        cout.precision(10);

do {
    system("CLS");
    cout << "Please set limits of integration separated by a space: ";
    cin >> a >> b;
    cout << "Please set number of parabolas to estimate with: ";
    cin >> p;
    cout << endl;
    cout << "Range of integration will be divided into " << p*2 << " divisions (n=" << p*2 << "). \nIntegral will be"
         << " estimated with " << p << " parabolas." << endl << endl;
    system("PAUSE");

    n=2*p; //two divisions for each parabola
    dx = (b-a)/n; //dx is length of each division

    int coef=0;
    double series=0;

    cout << "Series looks like: " << endl;
    for (int i=0; i<=n; i++)
    {
        coef = choose_coef(i,n);
        series += coef*f(a+(dx*i));
        cout << coef << " * " << "f(" << a+(dx*i) << ") +" << endl;
    }

    cout << "dx/3 = " << dx/3 << endl;
    cout << "series = " << series << endl;
    cout << endl << "Definite integral = " << (dx/3)*(series);
    cout << endl << endl << "Repeat? y/n: ";
    cin >> ans;
} while (ans == 'y' || ans == 'Y');














cout << endl << endl << endl;
return 0;
}