Math.lab7

#include <stdio.h>
#include <math.h>
/*
    \int_0^1 1/(2+x^3)
    f(x) = 1/(2+x^3)
*/
float rectangle(float a, float b, float N);
float f(float x);
float f_2(float x);
float find_M(float a, float b);

int main(int argc, char **argv)
{
    float N = 10;
    float a = 0;
    float b = 1;
    float h;
    h = (b - a) / N;

    float S = rectangle(a,b,N);
    float M = find_M(a,b);
    float R = M * pow(h,2)*(b-a) / 24;
    printf("S = %f\n", S);
    printf("M = %f\n", M);
    printf("R <= %f\n", R);

    return 0;
}

float rectangle(float a, float b, float N)
{
    int i;
    float h = (b - a) / N;
    float S = 0, x_i, x_i2;

    for (i = 1; i <= N; i++) {
        x_i = a + i*h;
        x_i2 = x_i - 0.5*h;
        S += f(x_i2)*h;
    }

    return S;
}

float f(float x)
{
    return 1/(2 + pow(x, 3));
}

float find_M(float a, float b)
{
    float max, Max;

    max = (f_2(a) > f_2(b)) ? f_2(a) : f_2(b);
    Max = (max > f_2((b-a)/2)) ? max : f_2((b-a)/2);

    return Max;
}

float f_2(float x)
{
    return fabs((-12*x*(1 - pow(x, 3))) / pow((2+pow(x,3)), 3));
}