//LAB 3

//METHODOS GAUSS

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

double F(const double t)
{
    return exp(-(t + 3) / 4) + cos(7 * (t + 3) / 4) - 6 / (t - 5);
}

main()
{

    double I2 = (1. * F(0.577350269189626) + 1. * F(-0.577350269189626)) / 2;
    double I3 = (0.888888888888889 * F(0) + 0.555555555555556 * F(0.774596669241483) + 0.555555555555556 * F(-0.774596669241483)) / 2;
    double I5 = (0.568888888888889 * F(0) + 0.478628670499366 * F(0.538469310105683) + 0.478628670499366 * F(-0.538469310105683) + 0.236926885056189 * F(0.906179845938664) + 0.236926885056189 * F(-0.906179845938664)) / 2;
    printf("n=2 apot=%10.8f\nn=3 apot=%10.8f\nn=5 apot=%10.8f\n", I2, I3, I5);

    return 0;
}

//METHODOS TRAPEZIOY

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

double f(const double x)
{
    return exp(-x / 2) + cos(3.5 * x) - 3 / (x - 4);
}

double I(const int n, const double a, const double b)
{
    int i;
    const double h = (b - a) / n;
    double I = 0;
    for (i = 0; i <= n; ++i) {
        I += (i == 0 || i == n ? f(a + i * h) / 2 : f(a + i * h));
    }
    I *= h;
    return I;
}

main()
{

    double I1 = I(50, 1, 2), I2 = I(100, 1, 2);
    printf("a=%f b=%f\nn=%3d apot=%10.8f\nn=%3d apot=%10.8f\nerror=%f\n", 1., 2., 50, I1, 100, I2, fabs(I1 - I2));

    return 0;
}

//METHODOS SIMSON

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

double f(const double x)
{
    return exp(-x / 2) + cos(3.5 * x) - 3 / (x - 4);
}

double I(const int n, const double a, const double b)
{
    int i;
    const double h = (b - a) / n;
    double I = 0;
    for (i = 0; i <= n; ++i) {
        if (i == 0 || i == n) {
            I += f(a + i * h);
        } else if (i % 2 == 0) {
            I += 2 * f(a + i * h);
        } else {
            I += 4 * f(a + i * h);
        }
    }
    I *= h / 3;
    return I;
}

main()
{

    double I1 = I(50, 1, 2), I2 = I(100, 1, 2);
    printf("a=%f b=%f\nn=%3d apot=%10.8f\nn=%3d apot=%10.8f\nerror=%.10f\n", 1., 2., 50, I1, 100, I2, fabs(I1 - I2));

}