CODE:

double func(double x)
{
	return sqrt(1 - x * x);
}

CODE:

// Fourier.h
#include 
#include 

static const double PI = 3.1415926535897932384626;

double integral(double (*func)(double x), double dx, double begin, double x, double (*func2)(double x) = 0, double nn = 1);

class Fourier
{
public:
	Fourier(double _T, int _n, double (*_func)(double), double _dx)
		: T(_T), n(_n), func(_func), dx(_dx)
	{
		omg = 2 * PI / T;
		calceff();
	}

	double T;
	double (*func)(double);
	double dx; // used in integral. not eccential for this class.

private:
	int n;
	double omg;
	std::vector an;
	std::vector bn;

public:
	void Setn(int _n)
	{
		n = _n;
		calceff();
	}

	// main
	double calc(double x)
	{
		double sum = 0;

		for(int i = 0; i < n + 1; i++)
		{
			sum += an[i] * cos(i * omg * x) + bn[i] * sin(i * omg * x);
		}

		return sum;
	}

private:

	double a(int m)
	{
		double aa = 2 / T * integral(func, dx, -T / 2, T / 2, cos, m * omg);
		return m ? aa : aa / 2;
	}

	double b(int m)
	{
		return 2 / T * integral(func, dx, -T / 2, T / 2, sin, m * omg);
	}

	void calceff()
	{
		for(int i = 0; i < n + 1; i++)
		{
			an.push_back(a(i));
			bn.push_back(b(i));
		}
	}
};

double integral(double (*func)(double x), double dx, double begin, double x, double (*func2)(double x), double nn)
{
	bool flg = false;
	if(x < begin)
	{
		double tmp = x;
		x = begin;
		begin = tmp;
		flg = true;
	}

	int n = (int)((x - begin) / dx);

	double sum = 0;

	for(int i = 0; i < n; i++)
	{
		if(func2 != 0)
			sum += func(begin + i * dx) * func2((begin + i * dx) * nn) * dx;
		else
			sum += func(begin + i * dx) * dx;
	}

	if(func2 != 0)
		sum += func(begin + dx * n) * func2((begin + dx * n) * nn) * (x - begin - n * dx);
	else
		sum += func(begin + dx * n) * (x - begin - n * dx);

	if(flg)
		sum *= -1;

	return sum;
}