trepezidal

#include <bits/stdc++.h>
using namespace std;

// Function to integrate
double f(double x) {
    return x * x * x; // Example function x^2
}

// Trapezoidal rule function
double trapezoidal(double a, double b, int n) {
    double h = (b - a) / n; // Width of each trapezoid
    double sum = 0.5 * (f(a) + f(b)); // Sum of the first and last terms

    for (int i = 1; i < n; ++i) {
        double x = a + i * h; // Current x value
        sum = sum + f(x); // Add f(x_i)
    }

    return sum * h;
}

int main() {
    double a, b; // Integration limits
    int n; // Number of subdivisions

    // Input values
    cout << "Enter lower limit of integration: ";
    cin >> a;
    cout << "Enter upper limit of integration: ";
    cin >> b;
    cout << "Enter the number of subdivisions: ";
    cin >> n;

    // Calculate integral using trapezoidal rule
    double integral = trapezoidal(a, b, n);

    // Output result
    cout << "Approximate integral: " << integral << endl;

    return 0;
}