function S=Q3_2(n) %Midpoint

%Input data
a = 0 ;
b = 1;
N = 2^n;
h = (b-a)/N;
x = a+h:2*h:b-h;
f = sin(x) - 0.5.*(cos(1)-1).*x.^2;

%weight=(1,1,1,1,1,...,1,1,1,1)
w(1:N/2)=1;

%sum
S = (2*h)*w*f';

end

%for n=2:9
%log2( (Q3_2(n)-Q3_2(n+1))/(Q3_2(n+1)-Q3_2(n+2)) )
%=  4.00751556485384
%=  4.00187356722385
%=  4.00046803935771
%=  4.00011743941228
%=  4.00002821894882
%=  3.99975887404869
%=  3.99942556437987
%=  4.19508507534071
%error = O(h^4)