ASD10_Integr_Trap_Simpson

// ASD10_Integr_Trap.cpp: определяет точку входа для консольного приложения.
//

#include "stdafx.h"
#include <iostream>
#include <math.h>
using namespace std;

double f(double x)
{
	return 2*log(cos(x)+2)-1;
}

double trap(double a, double b, int n)
{
	double h = (double)(b-a)/n, s = 0;
	for(int i = 1; i <= n-1; i++)
	{
		s += f(a+i*h);
	}
	return h * (f(a) + f(b))/2 + s;
}

double simpson(double a, double b, int n) // чётное n => результат менее точный
{
	double h = (b-a)/n, s = 0;
	for(int i = 1; i <= n-2; i += 2)
	{
		s += (2 * f(a+i*h) + 4*f(a+(i+1)*h))/3;
	}
	return h * ((f(a) + f(b))/2 + s);
}

int _tmain(int argc, _TCHAR* argv[])
{
	int n = 10;
	double a = 0, b = 100;
	double result = trap(a, b, n);
	cout << "Trap (n = " << n << "): " << result << endl;
	n = 11;
	result = simpson(a, b, n);
	cout << "Simpson (n = " << n << "): " << result << endl;
	cout << endl;

	n = 20;
	result = trap(a, b, n);
	cout << "Trap (n = " << n << "): " << result << endl;
	n = 21;
	result = simpson(a, b, n);
	cout << "Simpson (n = " << n << "): " << result << endl;
	cout << endl;

	n = 50;
	result = trap(a, b, n);
	cout << "Trap (n = " << n << "): " << result << endl;
	n = 51;
	result = simpson(a, b, n);
	cout << "Simpson (n = " << n << "): " << result << endl;
	cout << endl;

	system("PAUSE");
	return 0;
}