tixing.cpp

复化梯形公式计算积分的通用程序

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

//#define f(x) sin(x)
//#define I(x) cos(x)

#define f(x) log(x)
#define I(x) 1/x

double tixing(double up,double down,int n)
{
	double T,temp = 0;
	double h = (up - down)/n;
	for(int i=1;i<=n-1;i++)
	{
		temp += f(down+i*h);
	}
	T = h * ( f(down)/2 + temp + f(up)/2 );
	return T;
}

double error(double up,double down,double T)
{
	double P = I(down) - I(up);
	return P - T;
}

int main()
{
	double up,down;
	cout<<"Please input the up boundary and the down boundary:"<<endl;
	cin>>up;
	cin>>down;

	cout.precision(18);
	cout.setf(ios::fixed);

	cout<<0.346574/2+log(1.5)/2<<endl;

	for(int k=0;k<=12;k++)
	{
		int n = pow(2,k);
		double T = tixing(up,down,n);
		cout<<"When k = "<<k<<":"<<endl;
		cout<<"复化梯形积分可得结果为: "<<T<<endl;
		cout<<" ********** AND 误差为:  "<<error(up,down,T)<<endl;
	}
	return 0;
}