数值逼近
将区间[0,1]四等分，分别用复化梯形公式和复化 Simpson 公式计算定积分
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f(x) 4.0 / (1 + (x) * (x))
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的近似值。
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#include<iostream>
using namespace std;
#include<stdio.h>
//显示中文
#define _CRT_SECURE_NO_WARNINGS
#include <windows.h>//用于函数SetConsoleOutputCP(65001);更改cmd编码为utf8
#define f(x) 4.0 / (1 + (x) * (x))
void test()
{
float h = (1.0 - 0) / 4, temp, xk, yk, xkh, ykh, xk1, yk1;
int i;
temp = f(0); xk = 0;
for (i = 1; i < 4; i++)
{
xk = xk + h;
temp = temp + 2 * f(xk);
}
temp = temp + f(1);
temp = temp * h / 2;
cout << endl;
cout << "复化梯形公式计算的结果：" << temp << endl;
temp = 0;
h = (1.0 - 0) / 2;
xk = 0;
yk = f(0);
for (i = 0; i < 2; i++)
{
xkh = xk + h / 2;
ykh = f(xkh);
xk1 = xk + h;
yk1 = f(xk1);
temp = temp + h * (yk + 4 * ykh + yk1) / 6;
xk = xk1;
yk = yk1;
}
cout << endl;
cout << "复化 Simpson 公式计算的结果：" << temp << endl;
cout << endl;
}
int main()
{
//显示中文
SetConsoleOutputCP(65001);
test();
system("pause");
return 0;
}
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