辛普生法

#include

#include"head.h"

#include

void?main() //主程序文件

{

double a,b;

int n,c,d=0;

double f_1,f_2,zs1,zs2; //f_1,f_2为算法计算的积分值；zs1为f1真实的积分值zs2为f2真实的积分值

cout<<"f1(x)=1+x*x f2(x)=1+x+x*x+x*x*x"<

cout<<"以下为求f1,f2的对应积分区间的积分"<

while(1)//循环语句

{

if(d!=2)//重新输入新的数据

{

cout<<"请输入下限a，上限b和n:";

cin>>a>>b>>n;

}

else //只改变n的值

{

cout<<"请输入n：";

cin>>n;

}

cout<<"梯形法求积分请按：1\n辛普法生求积分按：2"<>c;?

if(c!=1&&c!=2)//输入错误就重新输入

{

for(;;)

{

cout<<"错误请重新选择：";

cin>>c;

if(c==1||c==2)break;

}

}

if(c==1)//选择梯形法计算

{

f_1=integralt(a,b,n,f1);

f_2=integralt(a,b,n,f2);

zs1=realintegral(a,b,real1);

zs2=realintegral(a,b,real2);

cout<<"-------------------------------梯形法结果为

------------------------------"<

}

if(c==2)//选择辛普生法计算

{

f_1=integrals(a,b,n,f1);

f_2=integrals(a,b,n,f2);

zs1=realintegral(a,b,real1);

zs2=realintegral(a,b,real2);

cout<<"------------------------------辛普生法结果为

-----------------------------"<

}

cout<<"n\ta\tb\tf1\tf1误差\t\tf2\tf2误差"<

cout<

cout<<"重新输入请按：1\n只改变n的值请按：2\n推出请按：0"<>d;

if(d!=0&&d!=1&&d!=2)//当d输入错误时重新输入

{for(;;)

{

cout<<"错误请重新选择："; cin>>d;

if(d==1||d==2||d==3) break;

}

}

if(d==0)//结束循环体

{

cout<<"谢谢您的使用再见"<

break;

}

}

}

#include//函数f1和f2

double f1(double x)

{return 1+x*x;}

double f2(double x)

{return 1+x+x*x+x*x*x;}

#include//梯形法求积分算法

double integralt(double a,double b,int n,double (*f)(double))

{

double h,jf=0; h=(b-a)/n;

for(int i=1;i<=n;i++)

{

jf+=((*f)(a+i*h)+(*f)(a+(i-1)*h))*h/2.0;

}

return jf;

}

#include//辛普生法求积分算法

double integrals(double a,double b,int n,double(*f)(double))

{

double h,sj=0,sr=0; h=(b-a)/(2*n);

for(int i=1;i<=2*n-1;i=i+2) sj+=(*f)(a+i*h);

for(int j=2;j<=2*n-2;j+=2) sr+=(*f)(a+j*h);

return ((*f)(a)+(*f)(b)+4*sj+2*sr)*h/3;

}

#include//辛普生法求积分算法

double integrals(double a,double b,int n,double(*f)(double))

{

double h,sj=0,sr=0; h=(b-a)/(2*n);

for(int i=1;i<=2*n-1;i=i+2) sj+=(*f)(a+i*h);

for(int j=2;j<=2*n-2;j+=2) sr+=(*f)(a+j*h);

return ((*f)(a)+(*f)(b)+4*sj+2*sr)*h/3;

}

#include

double f1(double x);//声明f1函数

double f2(double x);//声明f2函数

double real1(double x);//声明real1函数

double real2(double x);//声明real2函数

double integrals(double a,double b,int n,double(*f)(double));//声明辛普生法函数

double integralt(double a,double b,int n,double (*f)(double));//声明梯形法函数

double realintegral(double a,double b,double(*r)(double));//声明牛顿莱布尼茨计算积分函数

2，

#include

#define HIGH1(a,b,n) (b-a)/n //宏定义

double F1(double x,double y,int z); 函数原型说明

double F2(double x,double y,int z);

double f1(double u);

double f2(double v);

double sum1(double c,double d,int e);

double sum2(double p,double q,int r);

#define HIGH2(a,b,n) (b-a)/(2*n) //宏定义

double F3(double x,double y,int z); //函数说明

double F4(double x,double y,int z);

double f3(double u);

double f4(double v);

double sum5(double p,double q,int r);

double sum6(double p,double q,int r);

double sum3(double c,double d,int e);

double sum4(double c,double d,int e);

void integralts(double x,double y,int z,double (*f)(double,double ,int)); void integralt(double x,double y,int z,double(*f)(double,double,int));

void main() //主函数

{

int n;

double a,b; //定义变量

cout<<"please input a,b,n= \n"; //输出提示

cin>>a>>b>>n;

cout<<"a="<

cout<<"梯形法："<

cout<<"intesum1=";

integralt(a,b,n,F1); //应用函数指针调用函数

cout<<"intesum2=";

integralt(a,b,n,F2); //应用函数指针调用函数

cout<<"辛普生法："<

cout<<"intesum1=";

integralts(a,b,n,F3); //应用函数指针调用函数

cout<<"intesum2=";

integralts(a,b,n,F4); //应用函数指针调用函数

}

void integralt(double x,double y,int z,double (*f)(double,double,int)) // 利用梯形法球定积分

{

double ff;

ff=(*f)(x,y,z); //用函数指针调用F1函数

cout<

}

double F1(double x,double y,int z)

{

double h,Y1; //定义局部变量

h=HIGH1(x,y,z); //调用宏定义

Y1=h/2*(f1(x)+f1(y)+2*sum1(x,y,z)); //梯形法公式 return Y1; //返回梯形法得到的1+x*x的定积分的值

}

double F2(double x,double y,int z)

{

double h,Y2; //定义局部变量

h=HIGH1(x,y,z); //调用宏定义

Y2=h/2*(f2(x)+f2(y)+2*sum2(x,y,z)); //梯形法公式，调用f2,sum2函数

return Y2; //返回梯形法得到的1+x+x*x+x*x*x 的定积分的值}

double f1(double u)

{

double y1; //定义变量

y1=u*u+1;

return y1; //返回值

}

double f2(double v)

{

double y2; //定义变量

y2=1+v+v*v+v*v*v;

return y2; //返回值

}

double sum1(double c,double d,int e)

{

double h=HIGH1(c,d,e); //调用宏定义 double s1=0; //定义变量

for(int i=1;i<=e-1;i++) //for循环

{

double g=c+i*h;

s1+=f1(g);

return s1; 返回值

}

double sum2(double p,double q,int r)

{

double h=HIGH1(p,q,r); //引用宏定义

double s2=0; //定义变量

for(int i=1;i<=r-1;i++) //for循环

{

double g=p+i*h;

s2+=f2(g);

}

return s2; //返回值

}

void integralts(double x,double y,int z,double (*f)(double,double ,int)) //辛普生法

{

double ff;

ff=(*f)(x,y,z); //函数指针

cout<

}

double F3(double x,double y,int z)

{

double h,Y1; //定义变量

h=HIGH2(x,y,z);

Y1=h/3*(f3(x)+f3(y)+4*sum5(x,y,z)+2*sum6(x,y,z)); //调用f3,sum5,sum6函数

return Y1; //返回值

}

double F4(double x,double y,int z)

{

double h,Y2;

h=HIGH2(x,y,z);

Y2=h/3*(f4(x)+f4(y)+4*sum3(x,y,z)+2*sum4(x,y,z));

return Y2;

double f3(double u)

{

double y1=1+u*u;

return y1;

}

double f4(double v)

{

double y2=1+v+v*v+v*v*v;

return y2;

}

double sum5(double p,double q,int r)

{

double h=HIGH2(p,q,r);

double s=0;

for(int i=1;i<=2*r-1;i+=2) //for循环 {

double g=p+i*h;

s+=f3(g);

}

return s;

}

double sum6(double p,double q,int r)

{

double h=HIGH2(p,q,r);

double s=0;

for(int i=2;i<=2*r-2;i+=2) //for循环

{

double g=p+i*h;

s+=f3(g);

}

return s;

}

double sum3(double c,double d,int e)

{

double h=HIGH2(c,d,e);

double s=0;

for(int i=1;i<=2*e-1;i+=2)

{

double g=c+i*h;

s+=f4(g);

}

return s;

}

double sum4(double c,double d,int e) {

double h=HIGH2(c,d,e);

double s=0;

for(int i=2;i<=2*e-2;i+=2)

{

double g=c+i*h;

s+=f4(g);

}

return s;

}