function err=Q5_2(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(1:N+1)=2;
for j = 1:N/2
	w(2*j) = w(2*j)*2;
end
w(1) = w(N+1) = 1;

%Sum
s = (h/3)*w*f';

%error
exact = 0.8170720599186167;
err = abs(exact-s);

end

%for n=2:12
% Q5_2(n)/Q5_2(n+1)
%=  10.1885680322002
%=  12.9009191320832
%=  14.8014553713465
%=  15.6396885314473
%=  15.9044314400104
%=  15.9756212751602
%=  15.9923032657172
%=  16.0531177829099
%=  14.8034188034188
%=  6.15789473684211
%=  1.05555555555556
%error = O(h^4)?

%If we integrate from 0 to 1 directly, then the result of error will be:
%=  2.38678254209964
%=  2.38247034429886
%=  2.38041786545756
%=  2.37941109208488
%=  2.37891157182918
%=  2.37866264766391
%=  2.37853837793067
%=  2.37847628899956
%=  2.37844525591952
%=  2.37842974238546
%=  2.37842198349467
%The order is lost.