/* calculation of integral trapezoidal method*/
#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

double f(double x) {return x - x*x + x*x*x - x*x*x*x + sin(x*13.)/13.;}
double fint(double x) {return x*x/2. - x*x*x/3. + x*x*x*x/4. - x*x*x*x*x/5. - cos(x*13.)/169.;}

int main()
{
    double fint_exact = fint(1.2)-fint(0.);

    double area = 0., h = 1E-4, x = 0.;
    double f0,f1,f2 = f(x);
    while(x<1.2-h*1.5) {
        f0 = f2;
        x += h;	f1 = f(x);
        x += h;	f2 = f(x);
        area += (f0+f1*4.+f2);
    }
    area *= (h/3.);

 	cout << "Exact: " << setprecision(18) << fint_exact << " Numerical: " << setprecision(18) << area << " diff: " << fabs(fint_exact-area) << endl;

}