Find more at https://solutionarium.notion.site/Integration-83e6598a44ca4160a533b18ab374610d

Integration.cpp

#include <iostream>
#include <cmath>
using namespace std;

double Function(double x){
    return sin(x);
}

double Trapezoid_1 (double a, double b, double N){     //методом трапеций 1
    double Integral = 0, delta_x = (b - a) / N;
    double SubSum = 0;

    for (int i=1; i<N; i++){
        SubSum += Function(a + i*delta_x);
    }

    return Integral = delta_x * (SubSum + (Function(b) + Function(a))/2 );
}

double Trapezoid_2 (double a, double b, double N){        //методом трапеций 2
    double Integral = 0, delta_x = (b - a) / N;
    for (int i=0; i<N; i++){
        Integral += delta_x * ((Function(a + i*delta_x)+ Function(a+ (i+1)*delta_x))/2);
    }
    return Integral;
}

double LeftRiemann (double a, double b, double N){      //Left Riemann sum
    double Integral = 0, delta_x = (b - a) / N;
    for (int i=0; i<N; i++){
        Integral += delta_x * Function(a + i * delta_x);
    }
    return Integral;
}

double RightRiemann (double a, double b, double N){     //Right Riemann sum
    double Integral = 0, delta_x = (b - a) / N;
    for (int i=1; i<=N; i++){
        Integral += delta_x * Function(a + i * delta_x);
    }
    return Integral;
}

double Midpoint (double a, double b, double N){     //Midpoint method
    double Integral = 0, delta_x = (b - a) / N;
    for (int i=1; i<N; i++){
        Integral += delta_x * Function(a + (2*i-1) * (delta_x)/2);
    }
    return Integral;
}

double Simpson (double a, double b, double N){        //Simpson's method
    double Integral = 0, delta_x = (b - a) / N;
    double SubSum_1 = 0, SubSum_2 = 0;
    for (int i=1; i<=(N/2 - 1); i++){
        SubSum_1 += Function(a + 2*i*delta_x);
    }
    for (int i=1; i<=(N/2); i++){
        SubSum_2 += Function(a + (2*i - 1)*delta_x);
    }
    return Integral = (delta_x/3) * (Function(a) + 2*SubSum_1 + 4*SubSum_2 + Function(b));
}

int main(){
    double a, b;
    int N, t;
    cout << "Правый конец = " << endl;
    cin >> a;
    cout << "Левый конец = " << endl;
    cin >> b;
    cout << "Количество разбиений N" << endl;
    cin >> N;

    cout << "Посчитать интеграл методом " << endl << "1. Трапеций 1" << endl << "2. Левая риманова сумма" << endl << "3. Правая риманова сумма" << endl << "4. Средняя точка" << endl << "5. Simpson's method" << endl << "6. Трапеций 2" << endl;
    cin >> t;
    cout << endl;

    switch (t){
        case 1:{
            cout << "Integral of f(x) from a to b = " << Trapezoid_1(a, b, N);
            break;
        }
        case 2:{
            cout << "Integral of f(x) from a to b = " << LeftRiemann(a, b, N);
            break;
        }
        case 3:{
            cout << "Integral of f(x) from a to b = " << RightRiemann(a, b, N);
            break;
        }
        case 4:{
            cout << "Integral of f(x) from a to b = " << Midpoint(a, b, N);
            break;
        }
        case 5:{
            again:
            if (N%2 == 0) {
                cout << "Integral of f(x) from a to b = " << Simpson(a, b, N);
            }
            else{
                cout << "N должно быть четным!" << endl;
                cout << "Количество разбиений N" << endl;
                cin >> N;
                goto again;
            }
            break;
        }
        case 6:{
            cout << "Integral of f(x) from a to b = " << Trapezoid_2(a, b, N);
            break;
        }
    }

}