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function [volume_aitken] = calcola_volume_aitken()

    Q = @(t) 2 * sin(pi*t/24).^2;

    n1 = 100;
    n2 = 2*n1;
    n3 = 2*n2;

    S1 = simpson_rule(Q, 0, 24, n1);
    S2 = simpson_rule(Q, 0, 24, n2);
    S3 = simpson_rule(Q, 0, 24, n3);

    volume_aitken = S3 + (S3 - S2)^2 / (S3-2*S2+S1);

    disp(volume_aitken);

end

function S = simpson_rule(f, a, b, n)
    h = (b-a)/n;
    x = linspace(a, b, n+1);
    y = f(x);

    coeff = ones(1, n+1); %[ 1 1 1 1 1 1 1]
    coeff(2:2:n) = 4; %[ 1 4 1 4 1 4 1]
    coeff(3:2:n-1) = 2; %[1 4 2 4 2 4 1]
    S = (h/3) * sum(coeff .* y);
end