% Sample file for improper integral in qualidying exam, Dec 2017.

%Input data
clear all;

a = 0;
b = 1;
b2 = sqrt( exp(1)-1);
s = ones(1,3);
s2 = ones(1,3);
nmin = 20; % needs to be even
for k=1:3
  n = nmin*2^k; 
  h = (b-a)/n;
  h2 = (b2-a)/n;
  x = a:h:b;
  f  = sqrt(exp(x)-1);
  y = a:h2:b2;
  f2  = 2*y.^2./(1+y.^2);

%weight=(1,4,2,4,2,...,4,2,4,1)
  w = ones(1,n+1);
  w(2:2:n)=4;
  w(3:2:n-1)=2;
  s(k) = (h/3)*w*f'; 
  s2(k) = (h2/3)*w*f2'; 
end
%Sum
s
rate_s = log2( (s(1)-s(2))/(s(2)-s(3)) )
s2
rate_s2 = log2( (s2(1)-s2(2))/(s2(2)-s2(3)) )

%s =  3.10933712650887