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

double trapez(double a, double b, double (*fun)(double));
double simpson(double a, double b, double (*fun)(double));
double fun(double x);
double g(double y);

int main()
{
//	int n;
	double a, b, h;
	printf("Enter lower limit:\n");
	scanf_s("%lf", &a);
	printf("Enter upper limit:\n");
	scanf_s("%lf", &b);
	//printf("Enter number of nodes:\n");
	//scanf_s("%d", &n);
	double s, t;
	double errT, errS;
	for(int n=10; n<=100; n+=10)
	{
		h = (double)(b - a) / (n - 1);
		s = 0;
		t = 0;
		for (int i = 0; i < (n-1); i++)
		{

			t += trapez(a + i * h, a + (i + 1) * h, (*fun));
			s += simpson(a + i * h, a + (i + 1) * h, (*fun));
		}

		printf("n=%d\nTrapez: %lf\n", n, t);
		printf("Simpson: %lf\n", s);

		errT = atan(b) - t;
		errS = atan(b) - s;
		printf("Error Trapezoidal: %lf\n", errT);
		printf("Error Simpsonal: %lf\n", errS);
	}
	return 0;
}

double trapez(double a, double b, double (*fun)(double))
{
	double v;
	v = 0.5 * (b - a) * (fun(a) + fun(b));
	return v;
}

double fun(double x)
{
	double v = g(x);
	return v;
}

double simpson(double a, double b, double (*fun)(double))
{
	double v;
	double c = (a + b) / 2;
	v = (1.0 / 6) * (b - a) * (fun(a) + 4 * fun(c) + fun(b));
	return v;
}

double g(double y)
{
	double z = 1. / (1 + (y * y));
	return z;
}