#include <iostream>
#include<stdio.h>
#include<math.h>
using namespace std;
/* Define the function to be integrated here: */
double f(double x)
{
	return x * x;
}

/*Function definition to perform integration by Trapezoidal Rule */
double trapezoidal(double f(double x), double a, double b, int n) {
	double x, h, sum = 0, integral;
	int i;
	h = fabs(b - a) / n;
	for (i = 1; i < n; i++) {
		x = a + i * h;
		sum = sum + f(x);
	}
	integral = (h / 2)*(f(a) + f(b) + 2 * sum);
	return integral;
}

/*Program begins*/
int main() {
	int n, i = 2;
	double a, b, h, eps, sum = 0, integral, integral_new;


	cout << "\nEnter the initial limit: ";
	cin >> a;
	cout << "\nenter the final limit: ";
	cin >> b;
	cout << "\nEnter the desired accuracy: ";
	cin >> eps;
	integral_new = trapezoidal(f, a, b, i);

	/* Perform integration by trapezoidal rule for different number of sub-intervals until they converge to the given accuracy:*/
	do {
		integral = integral_new;
		i++;
		integral_new = trapezoidal(f, a, b, i);
	} while (fabs(integral_new - integral) >= eps);

	/*Print the answer */
	cout << "The integral is: " << integral_new;
	cout << "with intervals:"<<i;
	system("pause");
	return 0;
}