#include <iostream>
#include <cmath>


// Parameter constants for integration
const double A = 0.0;  // Lower bound of integration interval
const double B = 1.0;  // Upper bound of integration interval
const int N = 10;      // Number of small intervals (larger = finer = more accurate)

// The function to be integrated: f(x) = cos(x)
double f(double x) {
	return cos(x);
}


int main() {
	
	// --------------------------------------------------
	// Numerical integration using Simpson's Rule
	// --------------------------------------------------
	
	const double delta = (B - A) / N;   // Width of a small interval (Delta x)
	double value = 0.0;                 // Result of integration (total area)
	
	for(int i=0; i<N; i++) {
		
		// X-coordinate of the left edge of the i-th interval
		double x = A + i * delta;
		
		// Output the integration result up to the current point
		std::cout << x << "\t" << value << std::endl;
		
		// Add the area of the i-th interval to the total
		value += ( f(x) + f(x+delta) + 4.0 * f(x+delta/2.0) ) * delta / 6.0;
	}
	
	// Output the final result of the integration
	std::cout << B << "\t" << value << std::endl;
	
	return 0;
}