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Integrator.cpp
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Integrator.cpp
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#include<iostream>
using namespace std;
#include<cmath>
#include<stdlib.h>
#include<stdio.h>
#include"Integrator.h"
void Integrator::display()
{
system("cls");
int sel=-1;
while(sel!=0)
{
system("cls");
cout<<"choice 1:sin(x)"<<endl;
cout<<"choice 2:cos(x)"<<endl;
cout<<"choice 3:x*sin(x)"<<endl;
cout<<"choice 4:x*cos(x)"<<endl;
cout<<"choice 0:结束"<<endl;
cout<<"请输入你的选择:";
cin>>sel;
choice=sel;
//double a,b;
cout<<"***输入积分上下限min,max的值用空格隔开***"<<endl;
cin>>min>>max;
cout<<"***下限min="<<min<<endl;
cout<<"***上限max="<<max<<endl;
int sel;
cout<<"请选择排序方式:"<<endl;
cout<<" ---- 梯形法1:1"<<endl;
cout<<" ---- 梯形法2:2"<<endl;
cout<<" ---- 左矩形法:3"<<endl;
cout<<" ---- 中矩形法:4"<<endl;
cout<<" ---- 右矩形法:5"<<endl;
cout<<" ---- 辛甫生法:6"<<endl;
cin>>sel;
switch(sel)
{
case 1:
inte();
break;
case 2:
trapezoid();
break;
case 3:
leftTangular();
break;
case 4:
midTangular();
break;
case 5:
rightTangular();
break;
case 6:
simpson();
break;
}
system("pause");
}
}
double Integrator::f(double x)
{
double y;
switch(choice)
{
case 1:
y=sin(x);
break;
case 2:
y=cos(x);
break;
case 3:
y=x*sin(x);
break;
case 4:
y=x*cos(x);
break;
case 0:
cout<<"结束!"<<endl;
exit(0);
break;
default:
cout<<"请输入正确的函数!"<<endl;
break;
}
return y;
}
void Integrator::inte()
{
int n;
double trace,sum=0,area,heightl=0,heighth=0,i,a=0;
cout<<"***在("<<min<<","<<max<<")上的定积分"<<endl;
cout<<"***请输入对区间的分割次数:";
cin>>n;
//trace=((double)max-(double)min)/n;
//trace=(max-min)/n;
trace=(static_cast<double>(max)-static_cast<double>(min))/n;//求出定义区间上的元素单位
a=(double)min;
for(i=0;i<=max;i+=trace)
{
heightl=f(a); //求出梯形左边
a+=trace;
heighth=f(a); //求出梯形右边
area=(((heightl+heighth)*trace)/2); //梯形面积元素
sum+=area;
}
cout<<"***结果如下:"<<endl;
cout<<"***在("<<min<<","<<max<<")上的定积分为"<<sum<<endl;
}
void Integrator::leftTangular()
{
int i,n; //为区间等分的个数,应尽可能大
double h;
double sum=0; //h为步长
cout<<"***在("<<min<<","<<max<<")上的定积分"<<endl;
cout<<"***请输入对区间的分割次数:";
cin>>n;
//h=((double)max-(double)min)/n;
//h=(max-min)/n;
h=(static_cast<double>(max)-static_cast<double>(min))/n; //步长的计算
sum=f(min)*h;
for(i=1;i<n;i++)
{
sum=sum+f(min+i*h)*h;
}
cout<<"***结果如下:"<<endl;
cout<<"***在("<<min<<","<<max<<")上的定积分为"<<sum<<endl;
}
void Integrator::midTangular()
{
int n,i;
double h;
double sum=0;
cout<<"***在("<<min<<","<<max<<")上的定积分"<<endl;
cout<<"***请输入对区间的分割次数:";
cin>>n;
//h=((double)max-(double)min)/n;
h=(static_cast<double>(max)-static_cast<double>(min))/n;//求出定义区间上的元素单位
sum=0.5*(f(min)+f(min+h))*h;
for(i=1;i<n;i++)
{
sum=sum+0.5*(f(min+i*h)+f(min+(i+1)*h))*h;
}
cout<<"***结果如下:"<<endl;
cout<<"***在("<<min<<","<<max<<")上的定积分为"<<sum<<endl;
}
void Integrator::rightTangular()
{
int n,i;
double h;
double sum=0;
cout<<"***在("<<min<<","<<max<<")上的定积分"<<endl;
cout<<"***请输入对区间的分割次数:";
cin>>n;
//h=((double)max-(double)min)/n;
h=(static_cast<double>(max)-static_cast<double>(min))/n;//求出定义区间上的元素单位
sum=f(min+h)*h;
for(i=1;i<n-1;i++)
{
sum=sum+f(min+(i+1*h))*h;
}
cout<<"***结果如下:"<<endl;
cout<<"***在("<<min<<","<<max<<")上的定积分为"<<sum<<endl;
}
void Integrator::trapezoid()
{
int n,i;
double h;
double sum=0;
cout<<"***在("<<min<<","<<max<<")上的定积分"<<endl;
cout<<"***请输入对区间的分割次数:";
cin>>n;
//h=((double)max-(double)min)/n;
h=(static_cast<double>(max)-static_cast<double>(min))/n;//求出定义区间上的元素单位
sum=0.5*(f(min)+f(min+h))*h;
for(i=1;i<n;i++)
{
sum=sum+0.5*(f(min+i*h)+f(min+(i+1)*h))*h;
}
cout<<"***结果如下:"<<endl;
cout<<"***在("<<min<<","<<max<<")上的定积分为"<<sum<<endl;
}
double Integrator::T(double x,double y,int z)
{
double h,Tn;
int i;
//h=(y-x)/(double)z;
h=(y-x)/(static_cast<double>(z));
Tn=(f(x)+f(y))/2;
for(i=1;i<z;i++)
Tn=Tn+f(x+i*h);
Tn=Tn*h;
return (Tn);
}
void Integrator::simpson()
{
double sum;
int n;
cout<<"***在("<<min<<","<<max<<")上的定积分"<<endl;
cout<<"***请输入对区间的分割次数:";
cin>>n;
sum=(4*T(min,max,2*n)-T(min,max,n))/3; //利用辛甫生公式求解定积分
cout<<"***结果如下:"<<endl;
cout<<"***在("<<min<<","<<max<<")上的定积分为"<<sum<<endl;
}