#include<iostream.h>
#include<math.h>
int n;
float f(float);
void main()
{
	float s;
	float AutoTrap(float (*)(float),float,float);
	s=AutoTrap(f,0.0,1.0);
	cout<<"T("<<n<<")="<<s<<endl;
}
float AutoTrap(float (*)(float),float a,float b)
{
	int i;
	float x,s,h=b-a;
	float t1,t2=h/2.0*(f(a)+f(b));
	n=1;
	do{
		s=0.0;
		t1=t2;		
		for(i=0;i<=n-1;i++)
		{
			x=a+i*h+h/2;
			s+=f(x);
		}
		t2=(t1+s*h)/2.0;
		n*=2;
		h/=2.0;
	}while( fabs(t2-t1)>1e-6);
	return t2;
}

float f(float x)
{
	return 1/(1+x*x);
}
//用變步長梯形法計算積分積分只要將函數定義為

/*float f(float x)
{
	if(x==0)
		return 1;
	else 
		return sin(x)/x;
}*/