a = -pi
b = 4*pi
n10 = 10
h10 = (b-a) / n10
% alappontok:
x10 = a:h10:b
%% fuggvenyertekek:
f10 = cos(x10/4)+2
%% trapez kepletbol a sulyozott osszeg:
s10 = 2*sum(f10) - f10(1) - f10(n10+1)
%% alternativ:
% s = f(1) + f(n+1)
% for i = 2:n
%   s += 2* f(i)
% endfor
%% alternativ 2, vektor index trukkozessel:
% s = sum(f) + sum( f(2:n) )
T10 = s10*h10/2
n5 = 5
h5 = (b-a)/n5
x5 = a:h5:b
% alternativ: x5 = x10(1:2:(n+1))
f5 = cos(x5/4)+2
% alternativ: f5 = f10(1:2:(n+1))
s5 = 2*sum(f5) - f5(1) - f5(n5+1)
T5 = s5*h5/2
% utolagos hiba
hiba = abs(T10-T5)