no1.c

#include "stdlib.h"
#include "stdio.h"
#include "math.h"

double f(double x);
double g1(double x);
double g2(double x);
double g4(double x);

const double eps = 0.001;
const double a = 0.0;
const double b = 1.0;

int main(int argc, char **argv) {
    double m1 = max(fabs(g1(a)), fabs(g1(b)));
    double m2 = max(fabs(g2(a)), fabs(g2(b)));
    double m4 = max(fabs(g4(a)), fabs(g4(b)));

    // Средние прямоугольники
    int n = round((b - a) / sqrt(eps * 24.0 / (m2 * (b - a))));
    double step = (b - a) / n;
    double s = 0;
    for (double x = a + step/2; x < b; x += step)
        s += f(x) * step;
    printf("А>> %f\n\n", s);

    // Левые прямоугольники
    n = round(m1*(b - a)*(b - a)/(2 * eps));
    step = (b - a) / n;
    s = 0;
    for (int i = 0; i < n; i++)
        s += f(a + i * step) * step;
    printf("Б(левая)>> %f\n", s);
    // Правые прямоугольники
    s = 0;
    for (int i = 1; i <= n; i++)
        s += f(a + i * step) * step;
    printf("Б(правая)>> %f\n\n", s);

    // Трапеции
    n = round((b - a) / sqrt(eps * 12.0 / (m2 * (b - a))));
    step = (b - a) / n;
    s = 0;
    double fA = f(a);
    for (int i = 1; i <= n; i++) {
        double fB = f(a + step*i);
        s += (fA + fB) / 2 * step;
        fA = fB;
    }
    printf("В>> %f\n\n", s);

    // Симпсон
    n = round((b - a) / sqrt(sqrt(eps * 180.0 / (m4 * (b - a)))));
    step = (b - a) / n;
    s = 0;
    fA = f(a);
    for (int i = 1; i <= n; i++) {
        double fMid = f(a + step*((double)i - 0.5));
        double fB = f(a + step*i);
        s += (step/6)*(fA + fMid*4 + fB);
        fA = fB;
    }
    printf("Г>> %f\n\n", s);

    return 0;
}

double f(double x) {
    return 2*x + 6*x*x*x*x*x;
}
double g1(double x) {
    return 2 + 30*x*x*x*x;
}
double g2(double x) {
    return 120*x*x*x;
}
double g4(double x) {
    return 720*x;
}