Интег

#define _CRT_SECTRE_NO_WARNINGS
#include <iostream>
#include <cmath>
#include <vector>
using namespace std;

double func(double x) {
    return sqrt(0.2 * x) * cos(0.02 * x);
}
vector<double> init(double n, double a, double b) {
    vector<double> ans;
    double step = (b - a) / n;
    for (int i = 0; i <= n+1; i++) {
        if (!ans.size()) {
            ans.push_back(step);
        }
        else {
            ans.push_back(a);
            a += step;
        }
    }
    return ans;
}
void output(vector<double> vec) {
    printf("For %d intervals\n", vec.size() - 2);
    printf("Step = %.3lf\n", vec[0]);
    for (int i = 1; i < vec.size(); i++) {
        printf("%.3lf ", vec[i]);
        if (9 == (i - 1) % 10) {
            printf("\n");
        }
    }
    printf("\n");
}
double methodLeft(vector<double> nodes) {
    double sum = 0;
    for (int i = 1; i < nodes.size() - 1; i++) {
        sum += func(nodes[i]) * nodes[0];
    }
    return sum;
}
double methodRight(vector<double> nodes) {
    double sum = 0;
    for (int i = 2; i < nodes.size(); i++) {
        sum += func(nodes[i]) * nodes[0];
    }
    return sum;
}
double methodMiddle(vector<double> nodes) {
    double sum = 0;
    for (int i = 1; i < nodes.size() - 1; i++) {
        sum += 0.5 * (nodes[i+1] - nodes[i]) * (func(nodes[i]) + func(nodes[i + 1]));
    }
    return sum;
}
double methodSimpson(vector<double> nodes) {
    double sum = 0;
    for (int i = 1; i < nodes.size() - 1; i++) {
        sum += (nodes[i + 1] - nodes[i]) / 6.0 * (func(nodes[i]) + 4.0 * func(0.5 * (nodes[i + 1] + nodes[i])) + func(nodes[i + 1]));
    }
    return sum;
}

vector<double> iterate(vector<double> nodes) {
    vector<double> ans;
    ans.push_back(methodLeft(nodes));
    ans.push_back(methodRight(nodes));
    ans.push_back(methodMiddle(nodes));
    ans.push_back(methodSimpson(nodes));
    return ans;
}
int main() {
    double a = 1.0;
    double b = 3.0;
    double n[4] = { 4.0, 20.0, 100.0, 400.0 };
    vector<double> inter;
    vector <vector<double>> result;
    for (int i = 0; i < 4; i++) {
        inter = init(n[i], a, b);
        //output(inter);
        result.push_back(iterate(inter));
        inter.clear();
    }
    printf("%11.c |%6s    |%7s   |%8s  |%8s  |\n", ' ', "left", "right", "middle", "simpson");
    for (int i = 0; i < result.size(); i++) {
        printf("for n=%-5.0lf ", n[i]);
        for (int j = 0; j < result[i].size(); j++) {
            printf("|% 8.5lf  ", result[i][j]);
        }
        printf("|\n");
    }
    return 0;
}