coding UTF-8;         // Specify character encoding (to prevent garbled text)
import Math;          // Import the math function library
import tool.Graph2D;  // Import the graph plotting library


// Parameters 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 = better accuracy)

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

// ----------------------------------------------------------------------
// Numerical integration using the rectangular method (approximation)
// ----------------------------------------------------------------------

double delta = (B - A) / N;  // Width of each rectangle (Delta x)
double value = 0.0;          // Calculated integral value (total area of interval)

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 current x and integral value to the console
	println(x, value); // (Comment out if N is large, as it can be slow)
	
	// Add the area of the i-th rectangle to the total value
	value += f(x) * delta;
}

// Output the final integration result (total area)
println(B, value);

// Plot the contents of the console as a graph
// (Comment out if N is large, as it can be slow)
setGraph2DData(newGraph2D(), load());