#include <iostream>
#include <cmath>


// Parameter constants
const double A = 0.0;  // Lower bound of the integration interval
const double B = 1.0;  // Upper bound of the integration interval
const int N = 10;      // Number of subdivisions (higher = more accurate)

// Function to integrate: f(x) = cos(x)
double f(double x) {
	return cos(x);
}


int main() {
	
	// --------------------------------------------------
	// Numerical integration using the trapezoidal method
	// --------------------------------------------------
	
	const double delta = (B - A) / N;  // Width of each trapezoid: Delta x
	double value = 0.0;                // Final result (total area)
	
	for(int i=0; i<N; i++) {
		
		// X value at the bottom-left of the i-th trapezoid
		double x = A + i * delta;
		
		// Print partial result up to the i-th point
		std::cout << x << "\t" << value << std::endl;
		
		// Add the i-th trapezoid's area to the tota
		value += ( f(x) + f(x+delta) ) * delta / 2.0;
	}
	
	// Output final result
	std::cout << B << "\t" << value << std::endl;
	
	return 0;
}