//============================================================\\
//		VTrap 1.0
//	Implementation of the Trapezoidal Rule.
//	Integrates f(x) from b to a, n iterations.
//  n shoudl be within 1 to 
//	Written by V'lion 2002.
//	Contect me at pdn@rmci.net
//	Please visit my 4D engine site at http://thefivelions.tripod.com/bugle4d/
//============================================================//
#include <math.h>
#include <iostream.h>

/*
Implementation of the trapezoidal rule.
all var names are direct from it.
deltax = (b-a)/n
(deltax/2)(y0+2y1+...+2y(n-1) + yn)
*/

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

void main()
{
	double b, a, deltax, acc = 0;
	unsigned int n;
	cout << "Numerical integration according to the trapezoidal rule.\nRecommend n be a large number.\n";
	cout << "  /b\n"
		 << " /\n"
		 << " |\n"
		 << " | f(x) dx\n"
		 << " |\n"
		 << " /\n"
		 << "/a\n"
		 << "n is the iteration number.\n"
		 << "\n";
	cout << "b: ";
	cin >> b;
	cout << "a: ";
	cin >> a;
	cout << "n: ";
	cin >> n;

	//Error checks.
	if(b < a)
	{
		cout << "b less than a !"
			 << "Errornous result avoided."
			 << "Program shutting down.";
		return;
	}
	if(!n)
	{
		cout << "n is zero !\n"
			 << "Divide by zero avoided;\n"
			 << "Program shutting down.";
		return;
	}

	//DX calculated
	deltax = (b-a)/n;

	//Alg run.
	for(double i = a + deltax; i <= (b - deltax); i+= deltax)
	{
		acc += 2*f(i);
	}

	//Result calculated and displayed
	cout << "\n Definite integral from b to a of f(x) is: ";
	cout << ((deltax / 2) * ( f(a) + acc + f(b) ) )
		 << endl;
}