Homework task

area_calculation.c

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

#define F(x) (f(x)-g(x))
#define F1(x) (f1(x)-g1(x))

typedef double (*func)(double);

double root(func f, func g, func f1, func g1, double a, double b, double eps1)
{
    int right = F1(a) * (F1(b)-F1(a)) > 0;
    if(right)
        eps1 = -eps1;
    double c = right ? a : b;
    while(F(c)*F(c+eps1) > 0)
        c = c - F(c)/F1(c);
    return c;
}

double integral(func f, func g, double a, double b, double eps2)
{
    int N = 1;
    double oldI, I = -1.0;
    do
    {
        oldI = I;
        I = F(a) + F(b);
        double h = (b-a) / N;
        int i;
        for(i = 1; i < N; i++)
            if(i % 2)
                I += 2 * F(a+i*h);
            else
                I += 4 * F(a+i*h);
        I *= h/3;
        N *= 2;
    }
    while((N == 1) || (fabs(oldI - I) >= eps2 * 15));
    return I;
}

double ff(double x)
{
    return 0.35*x*x - 0.95*x + 2.7;
}
double ff1(double x)
{
    return 0.35*2*x - 0.95;
}
double gg(double x)
{
    return pow(3, x) + 1;
}
double gg1(double x)
{
    return log(3) * pow(3, x);
}
double hh(double x)
{
    return 1/(x+2);
}
double hh1(double x)
{
    return -1/(x+2)/(x+2);
}

int main()
{
    double
        x1 = root(hh, ff, hh1, ff1, -1.95, -1.5, 0.000001), // about -1.8
        x2 = root(gg, hh, gg1, hh1, -1.75, -1.0, 0.000001), // about -1.2
        x3 = root(ff, gg, ff1, gg1, -2.00, 1.00, 0.000001); // about 0.32
    printf("%f %f %f\n", x1, x2, x3);
    double res =
        integral(ff, hh, x1, x2, 0.000001) +
        integral(ff, gg, x2, x3, 0.000001); // about 3.94
    printf("%f\n", res);
    return 0;
}

Results:
-1.821137 -1.209384 0.324613
3.948069