function integral=Q5(n) %Simpson

%Input data
a = 0 ;
b = 2^(-1/4);
N = 2^n;
h = (b-a)/N;
x = a:h:b;
f = (1-x.^4).^(1/4);

%weight=(1,4,2,4,2,...,4,2,4,1)
w = zeros(1,N+1);
w(2:2:N) = 4;
w(3:2:N-1) = 2;
w(1) = w(end) = 1;

%Sum
s = (h/3)*w*f';
integral = 8*(s-2^(-3/2));

end

%for n=2:12
%abs(Q5(n)-Q5(n+1))
%=  0.00275356559143081
%=    2.76444174239110e-04
%=    2.16594489517163e-05
%=    1.46901508379926e-06
%=    9.40354665246446e-08
%=    5.91430016072536e-09
%=    3.70233621538318e-10
%=    2.31565877584217e-11
%=    1.43440814781570e-12
%=    8.70414851306123e-14
%=    8.88178419700125e-16
%for n=12, integral =3.70814935460273
%exact=                       3.70814935460274  (wolfram: 8*( \int_0^(2^(-1/4)) f(x)dx - 2^(-3/2) ) )