function err=Q3(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';

%error
exact = (7/6)*(1-cos(1));
err = abs(s-exact);

end

%for n=2:9
%Q3(n)/Q3(n+1) =  16.0795873185008
%Q3(n)/Q3(n+1) =  16.0198018597843
%Q3(n)/Q3(n+1) =  16.0049445102643
%Q3(n)/Q3(n+1) =  16.0012383884155
%Q3(n)/Q3(n+1) =  16.0002767303146
%Q3(n)/Q3(n+1) =  15.9997332764323
%Q3(n)/Q3(n+1) =  16.0359281437126
%Q3(n)/Q3(n+1) =  16.7000000000000
%error = O(h^4)