#include <iostream>
#include <cmath>


// Parameter constants for the calculation
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 rectangles (more = finer steps = higher accuracy)

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


int main() {
	
	// ----------------------------------------------------------------------
	// Numerical integration using the rectangular method (approximation)
	// ----------------------------------------------------------------------
	
	const double delta = (B - A) / N;  // Width of each rectangle (Delta x)
	double value = 0.0;                // Calculated integral value (total area)
	
	for(int i=0; i<N; i++) {
		
		// X-value at the lower-left corner of the i-th rectangle
		double x = A + i * delta;
		
		// Output the integral value at this point
		std::cout << x << "\t" << value << std::endl;
		
		// Add the area of the i-th rectangle to the total
		value += f(x) * delta;
	}
	
	// Output the final integration result (total area)
	std::cout << B << "\t" << value << std::endl;
	
	return 0;
}