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

// =======================================================================
// Settings for Integrations
// =======================================================================

// The tntegrant function.
double f(double x) {
	return x * cos(x);
}

double A = 0.0;  // The lower-limit of the integration interval.
double B = 40.0; // The upper-limit of the integration interval.
int N = 10000;   // The number of tiny intervals for numerical integration.

// Be careful of the maximum limit of the "int" value in C programming language.
// It depends on your environment, and it might be smaller than you thought.
// Use "long long" or "int64_t" and so on, instead of "int", if necessary.


// =======================================================================
// Settings for Plottings
// =======================================================================

int PRINT_POINTS = 1000; // Number of points to be plotted (*).

// *) Actually, the number of plotted points will be PRINT_POINTS + 1,
//    because the last one point will be output after when integration loops ended.
//    Also, if N is indivisible by PRINT_POINTS, the actual number of plotted points 
//    will be larger/smaller than PRINT_POINTS in some extent.


// =======================================================================
// Compute The Integral Value Numerically
// =======================================================================

int main() {
	double delta = (B - A) / N;  // The width of a tiny interval.
	double value = 0.0;  // Add approximated area of all tiny intervals to this variable.
	int print_interval = N / PRINT_POINTS; // Loop-intervals between points to be plotted.

	// Traverse tiny intervals from lower-limit (left) to upper-limit (right).
	for(int i=0; i<N; ++i) {

		// The x-coordinate value of the left-bottom point of i-th tiny interval.
		double x = A + i * delta;

		// Output coordinate values of a point, at every print_interval cycles.
		if (i % print_interval == 0) {
			printf("%lf\t%lf\n", x, value);
		}

		// -------------------------------------------------------------------
		// Compute area of i-th tiny interval approximately
		// (select a rule from the following), 
		// and add it to the variable "value".
		// -------------------------------------------------------------------

		// Use rectangular method (approximates area of an interval as a rectangle):
		// value += f(x) * delta;

		// Use trapezoidal method (approximates area of an interval as a trapezoid):
		// value += ( f(x) + f(x+delta) ) * delta / 2.0;

		// Use Simpson's rule (approximates f(x) in an interval as a quadratic function):
		value += ( f(x) + f(x+delta) + 4.0 * f(x+delta/2.0) ) * delta / 6.0;
	}

	// Output the computed integral value (sum of area of all tiny intervals).
	printf("%lf\t%lf\n", B, value);

	return 0;
}