梯形公式,辛浦生(辛普生)公式求函数积分

#include"iostream.h"

#include"math.h"

class tixing //梯形类

{

public:

     tixing();//初始化

     void SetValue(double LowLimit1,double UpLimit1);//设置积分上下限值

     double f(double x);//函数f(x)

     virtual double Result(void);//积分结果,虚函数

     virtual void wucha(void);//误差范围,虚函数

protected:

     double LowLimit;//上限

     double UpLimit;//下限

};

 

tixing::tixing()

{

     LowLimit=0.0;//初始值

     UpLimit=0.0;

}

 

void tixing::SetValue(double LowLimit1,double UpLimit1)//设置函数

{

     LowLimit=LowLimit1;

     UpLimit=UpLimit1;

}

 

double tixing::f(double x)

{

 return exp(-x);//本例f(x)为e^(-x)
}

 

double tixing::Result(void)

{
    
 return (UpLimit-LowLimit)/2*(f(LowLimit)+f(UpLimit));//梯形公式

}

void tixing::wucha(void)

{
  double x;
  x=-pow((UpLimit-LowLimit),3)/12*(-f(LowLimit));//梯形误差公式
  cout<<"梯形公式误差范围<="<<x<<endl;
}

class xinpusheng:public tixing{//辛浦生类,从梯形继承
public:
 virtual double Result(void);//对结果重新定义(因为公式不同)
 virtual void wucha(void);//同上,对误差重新定义

};
double xinpusheng::Result(void)//结果

{
    
return (UpLimit-LowLimit)*(f(LowLimit)+4*f((LowLimit+UpLimit)/2.0)+f(UpLimit))/6.0;

}

void xinpusheng::wucha(void)//误差

{
  double x;
  x=-pow((UpLimit-LowLimit),5)/2880*(-f(LowLimit));
  cout<<"wucha:";
  if (x<0){
  x=-x;
  }
  cout<<"辛浦生公式误差范围<=:"<<x<<endl;
}

int main(void)

{

     double LowLimit1=0.0,UpLimit1=0.0;

     tixing tixing1;//梯形对象
 
  xinpusheng xinpusheng1;//辛浦生对象

     cout<<"f(x)=e^(-x)"<<endl;

  cout<<"请输入积分上限:";

     cin>>UpLimit1;
    
  cout<<"请输入积分下限:";

     cin>>LowLimit1;

    

     tixing1.SetValue(LowLimit1,UpLimit1);//梯形赋值
  xinpusheng1.SetValue(LowLimit1,UpLimit1);//辛浦生赋值
 
 
     cout<<"积分结果: 梯形"<<tixing1.Result()<<endl;
     tixing1.wucha();
 
     cout<<"积分结果: 辛浦生"<<xinpusheng1.Result()<<endl;
     xinpusheng1.wucha(); 
 

     return 0;

}

#include"iostream.h"

#include"math.h"

class tixing //梯形类

{

public:

     tixing();//初始化

     void SetValue(double LowLimit1,double UpLimit1);//设置积分上下限值

     double f(double x);//函数f(x)

     virtual double Result(void);//积分结果,虚函数

     virtual void wucha(void);//误差范围,虚函数

protected:

     double LowLimit;//上限

     double UpLimit;//下限

};

 

tixing::tixing()

{

     LowLimit=0.0;//初始值

     UpLimit=0.0;

}

 

void tixing::SetValue(double LowLimit1,double UpLimit1)//设置函数

{

     LowLimit=LowLimit1;

     UpLimit=UpLimit1;

}

 

double tixing::f(double x)

{

 return exp(-x);//本例f(x)为e^(-x)
}

 

double tixing::Result(void)

{
    
 return (UpLimit-LowLimit)/2*(f(LowLimit)+f(UpLimit));//梯形公式

}

void tixing::wucha(void)

{
  double x;
  x=-pow((UpLimit-LowLimit),3)/12*(-f(LowLimit));//梯形误差公式
  cout<<"梯形公式误差范围<="<<x<<endl;
}

class xinpusheng:public tixing{//辛浦生类,从梯形继承
public:
 virtual double Result(void);//对结果重新定义(因为公式不同)
 virtual void wucha(void);//同上,对误差重新定义

};
double xinpusheng::Result(void)//结果

{
    
return (UpLimit-LowLimit)*(f(LowLimit)+4*f((LowLimit+UpLimit)/2.0)+f(UpLimit))/6.0;

}

void xinpusheng::wucha(void)//误差

{
  double x;
  x=-pow((UpLimit-LowLimit),5)/2880*(-f(LowLimit));
  cout<<"wucha:";
  if (x<0){
  x=-x;
  }
  cout<<"辛浦生公式误差范围<=:"<<x<<endl;
}

int main(void)

{

     double LowLimit1=0.0,UpLimit1=0.0;

     tixing tixing1;//梯形对象
 
  xinpusheng xinpusheng1;//辛浦生对象

     cout<<"f(x)=e^(-x)"<<endl;

  cout<<"请输入积分上限:";

     cin>>UpLimit1;
    
  cout<<"请输入积分下限:";

     cin>>LowLimit1;

    

     tixing1.SetValue(LowLimit1,UpLimit1);//梯形赋值
  xinpusheng1.SetValue(LowLimit1,UpLimit1);//辛浦生赋值
 
 
     cout<<"积分结果: 梯形"<<tixing1.Result()<<endl;
     tixing1.wucha();
 
     cout<<"积分结果: 辛浦生"<<xinpusheng1.Result()<<endl;
     xinpusheng1.wucha(); 
 

     return 0;

}

//计算方法,数值分析中的梯形积分公式,辛浦生积分公式,简称梯形公式,辛浦生公式求函数f(x)=e^(-x)在积分上下限//
//为1~0的范围内的积分,并算出了各自算法的误差.
//下面是对上面的代码简化

#include"iostream.h"

#include"math.h"

double f(double x)

{

 return exp(-x);//本例f(x)为e^(-x)
}

 

double tixingResult(double UpLimit,double LowLimit)

{
    
 return (UpLimit-LowLimit)/2*(f(LowLimit)+f(UpLimit));//梯形公式

}

void tixingwucha(double UpLimit,double LowLimit)

{
  double x;
  x=-pow((UpLimit-LowLimit),3)/12*(-f(LowLimit));//梯形误差公式
  cout<<"梯形公式误差范围<="<<x<<endl;
}

double xinpushengResult(double UpLimit,double LowLimit)//结果

{
    
return (UpLimit-LowLimit)*(f(LowLimit)+4*f((LowLimit+UpLimit)/2.0)+f(UpLimit))/6.0;

}

void xinpushengwucha(double UpLimit,double LowLimit)//误差

{
  double x;
  x=-pow((UpLimit-LowLimit),5)/2880*(-f(LowLimit));
  cout<<"wucha:";
  if (x<0){
  x=-x;
  }
  cout<<"辛浦生公式误差范围<=:"<<x<<endl;
}

int main(void)

{

     double LowLimit,UpLimit;

     cout<<"f(x)=e^(-x)"<<endl;

  cout<<"请输入积分上限:";

     cin>>UpLimit;
    
  cout<<"请输入积分下限:";

     cin>>LowLimit;

 
     cout<<"积分结果: 梯形"<<tixingResult(UpLimit,LowLimit)<<endl;
     tixingwucha(UpLimit,LowLimit);
 
     cout<<"积分结果: 辛浦生"<<xinpushengResult(UpLimit,LowLimit)<<endl;
     xinpushengwucha(UpLimit,LowLimit); 
 

     return 0;

}

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