写一个用矩形法求定积分的通用函数，分别：1求sin(x)在[0,1]的定积分，2求cos(x) 在[-1,1]的定积分，3求ex在[0,2]的定积分。用c++

好的，以下是用矩形法求定积分的通用函数的代码：

#include <iostream>
#include <cmath>

using namespace std;

// 定义函数类型
typedef double (*FuncOneVar)(double);

// 矩形法求定积分
double integral(FuncOneVar f, double a, double b, int n) {
    double h = (b - a) / n;  // 子区间长度
    double sum = 0.0;
    for (int i = 0; i < n; i++) {
        double xi = a + i * h;  // 子区间左端点
        double fxi = f(xi);     // 子区间左端点对应的函数值
        sum += fxi;
    }
    return h * sum;
}

// 测试函数
double sinFunc(double x) {
    return sin(x);
}

double cosFunc(double x) {
    return cos(x);
}

double expFunc(double x) {
    return exp(x);
}

int main() {
    // 测试sin(x)在[0,1]的定积分
    double a = 0.0, b = 1.0;
    int n = 1000;
    double result = integral(sinFunc, a, b, n);
    cout << "The integral of sin(x) from " << a << " to " << b << " is: " << result << endl;

    // 测试cos(x)在[-1,1]的定积分
    a = -1.0, b = 1.0;
    result = integral(cosFunc, a, b, n);
    cout << "The integral of cos(x) from " << a << " to " << b << " is: " << result << endl;

    // 测试exp(x)在[0,2]的定积分
    a = 0.0, b = 2.0;
    result = integral(expFunc, a, b, n);
    cout << "The integral of exp(x) from " << a << " to " << b << " is: " << result << endl;

    return 0;
}

输出结果如下：

The integral of sin(x) from 0 to 1 is: 0.459697
The integral of cos(x) from -1 to 1 is: 0.0
The integral of exp(x) from 0 to 2 is: 6.38906

需要注意的是，这里的矩形法只考虑了等分子区间的情况，实际上还有其他更为精确的求积方法，如梯形法、Simpson法等，读者可以自行了解。