a = 0;
b = 1;
tol = 1.0E-05; %desired tolerance


% function to integrate and its antiderivative
f = @(x) sqrt(x);
F = @(x) 2/3*x^(3/2);

%f = @(x) 1./sqrt(x);
%F = @(x) 2*sqrt(x);

%f = @(x) sin(exp(6*(x-0.5)));

I_exact = F(b)-F(a);
fprintf('Exact integral = %15.10e\n', I_exact);


%% Plot the function
Xf = linspace(a,b,500);
figure(1); clf;
fs = 24; %font size
plot(Xf,f(Xf),'-',...
     'LineWidth',3,'MarkerSize',10);
xlabel('x','FontSize',fs); ylabel('f(x)','FontSize',fs); 
grid on;

[I,m]=uniform_refinement(f,F,a,b);
%[I,m]=adaptive_fake(f,F,a,b,tol);
%[I,m]=adaptive_real(f,a,b,tol);

fprintf('Integral ~ %15.10e, error = %e, #elements = %d\n', I,abs(I-I_exact),m);

% Implementation from the book
%[I]=adapquad(f,a,b,tol);
%fprintf('Integral ~ %15.10e, error = %e\n', I,abs(I-I_exact));