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

// Our function to integrate over
double ourfunc(double x) {
  return x*x;
}

typedef double (*DfD) (double);

// Simpson's parabola method
double simpsons_int(DfD f,
            double x0, double x1, int n){
  double x, sum, dx = (x1 - x0) / n;
  sum = f(x1) - f(x0);

  for(x = x0; x+dx/2 < x1; x += dx)
    sum += 2.0 * f(x) +
           4.0 * f(x + dx/2);

  return sum * dx / 6.0;
}

// Midpoint Rectangle Method
double midpoint_int (DfD f,
                double x0, double x1, int n){
  int i;
  double x, dx, sum = 0.0;
  dx = (x1-x0)/ n;
  for (i = 0, x = x0 + dx/2; i < n;
       i++, x += dx)
    sum += f(x);
  return sum * dx;
}

// Trapezoidal Line method
double trapezoidal_int (DfD f,
            double x0, double x1, int n){
  double x, dx, sum;
  int i;
  dx = (x1-x0)/ n;
  sum = (f(x0) + f(x1))/2;
  for (i=1, x = x0 + dx; i < n; 
			i++, x += dx)
    sum += f(x);
  return sum * dx;
}


int main() {
	int sx = 0; // start point
	int fx = 2; // end point of interval
	int n = 2; // number of segments

	printf("Start Point: %d\n", sx);
	printf("End Point:   %d\n", fx);
	printf("Segments:    %d\n", n);
	printf("Seg. Width:  %g\n\n", (((double)fx-sx)/n));
	printf("Midpoint:  %f\n", midpoint_int(ourfunc, sx, fx, n));
	printf("Simpsons:  %f\n", simpsons_int(ourfunc, sx, fx, n));
	printf("Trapezoid: %f\n", trapezoidal_int(ourfunc, sx, fx, n));

	return 0;
}