#include <stdio.h>
#include <math.h>


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

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


int main(void) {
	
	// --------------------------------------------------
	// Numerical integration using the trapezoidal method
	// --------------------------------------------------
	
	double delta = (B - A) / N;  // Width of each trapezoid: Delta x
	double value = 0.0;          // Final result (total area)
	int i;
	
	for(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
		printf("%f\t%f\n", x, value);
		
		// Add the i-th trapezoid's area to the total
		value += ( f(x) + f(x+delta) ) * delta / 2.0;
	}
	
	// Output final result
	printf("%f\t%f\n", B, value);
	
	return 0;
}