Адаптивный

#include <stdio.h>
#include <math.h>

#define MAX_ITER 1000
#define EPSILON 1e-6

double f(double x) {
    return sqrt(1 + pow(x, 5));
}

double trapezoidal(double a, double b, int n, double (*func)(double)) {
    double h = (b - a) / n;
    double sum = 0.5 * (func(a) + func(b));
    for (int i = 1; i < n; i++) {
        sum += func(a + i * h);
    }
    return h * sum;
}

double runge(double a, double b, double epsilon, double (*func)(double)) {
    double h = b - a;
    double I1 = trapezoidal(a, b, 2, func);
    double I2 = trapezoidal(a, b, 4, func);
    double delta = fabs(I2 - I1) / 3.0;
    int iter = 0;

    while (delta > epsilon && iter < MAX_ITER) {
        h /= 2;
        I1 = I2;
        I2 = trapezoidal(a, b, 4 * (iter + 1), func);
        delta = fabs(I2 - I1) / 3.0;
        iter++;
    }

    return I2;
}

int main() {
    double a, b, epsilon;
    printf("Enter the limits of integration (a, b): ");
    scanf("%lf%lf", &a, &b);
    printf("Enter the desired accuracy (epsilon): ");
    scanf("%lf", &epsilon);

    double result = runge(a, b, epsilon, f);
    printf("Approximate value of the integral: %.6lf\n", result);

    return 0;
}