v8 nansi

function [y] = zad2(t)
y = 2/sqrt(pi*2)*exp(-t.^2/2);

end



function I = trapezi(f, a, b, n)
h = (b-a)/n;
I = 0.5*(feval(f, a) + feval(f, b));

for i = 2:n
    I = I + feval(f, a+h*(i-1));
end

I = I * h;
end

function I = simpson(f, a, b, n)
h = (b-a)/n;
I = feval(f, a) + feval(f, b);
k = 4;
for i=2:n
    I = I + k * feval(f, a+h*(i-1));
    k = 6 - k;
end
I = h/3 * I;


end


function I = romberg(f, a, b, itmax, errmax)
k = 0;
N(1) = trapezi(f, a, b, 2^k);
for it = 1:itmax
    k = k+1;
    T(1) = trapezi(f, a, b, 2^k);
    for m = 1:k
        T(m+1) = (4^m*T(m)-N(m))/(4^m-1);
        I = T(m+1);
        if (abs(I-T(m) < errmax))
            return;
        end
    end
    N = T;
end

end