Calculating errors of both montecarlo and trapezoid integration based on precalculated real value.

monteCarloAndTrapezoidIntegration.cpp

#include <iostream>
#include <cstdlib>
#include <time.h>



double f(double x) {
	return x*x;
}

double monteCarlo(int start, int stop, double N) {
	double avarageValue=0.0;
	for (int i = 0; i < N; i++) avarageValue += f(rand() / (double)RAND_MAX * 8 + 2);

	return (avarageValue/N)*(stop-start);
}

double integralTrapezoid(int start,int stop,double N) {
	double dx = (stop - start) / N;
	double S=0.0;
	for (int i = 1; i < N; i++) {
		S += ((f(start + (i*dx)) + f(start + ((i - 1)*dx)))*dx) / 2;
	}
	return S;
}

double calculateError(double real, double expected) {
	return expected - real;
}

int main() {
	srand(time(NULL));
	std::cout << "Monte Carlo: " << std::endl;
	std::cout << calculateError(monteCarlo(2, 10, 10), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(monteCarlo(2, 10, 100), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(monteCarlo(2, 10, 1000), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(monteCarlo(2, 10, 10000), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(monteCarlo(2, 10, 1000000), 330.0 + (2.0 / 3.0)) << std::endl;

	std::cout << "Trapezoid: " << std::endl;
	std::cout << calculateError(integralTrapezoid(2, 10, 10), 330.0+(2.0/3.0)) << std::endl;
	std::cout << calculateError(integralTrapezoid(2, 10, 100), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(integralTrapezoid(2, 10, 1000), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(integralTrapezoid(2, 10, 10000), 330.0 + (2.0 / 3.0)) << std::endl;
	std::cout << calculateError(integralTrapezoid(2, 10, 100000), 330.0 + (2.0 / 3.0)) << std::endl;

	system("pause");

}