#include <iostream>
#include <cmath>
using namespace std;

double f(double x) {
   // f(x) = x*x
  return x * x * sin(x);
}


double trapezint(double a, double b, int N) {

	// funkcija naj bo kar f(x)=x^2

	double s=0;
	s = ( f(a) + f(b) )/2;
	
	double h = ( b - a ) / N;
	for ( int i=1 ; i < N ; i++ ) {
	   double xi = a + i * h ;
	   s = s + f(xi);
	}
	
	s = s * h;
	return s;


}

double simpsonint(double a, double b, int N) {

	// funkcija naj bo kar f(x)=x^2

	double s=0;
	
	double h = ( b - a ) / N;
	double fac=1;
	for ( int i=1 ; i < N ; i++ ) {
	   double xi = a + i * h ;
	   fac=2;
	   if ( i % 2 == 0 ) { fac = 1;  }  
	   s = s + fac*f(xi);
	}
	s=2. * s  +  ( f(a) + f(b) ) ;
	
	s = s/3;

	s = s * h;
	return s;


}

int main() {


	int N=50;
	double a=0;
	double b=1;


	cout << "trapezna=" << trapezint(a,b,N) << endl;
	printf("natancno = %30.20f\n",trapezint(a,b,N));
	cout << "simpsonova=" << simpsonint(a,b,N) << endl;
	printf("natancno %30.20f\n",simpsonint(a,b,N));


}