clear

%%
% Consider the integral
% 
% \int_{-1}^1 \frac{1}{1+4x^2} \, dx = \arctan(2).
% 
f = @(x) 1./(1 + 4*x.^2);
exact = atan(2);

%%
% We compare the two spectral integration methods for a range of n values.
n = (8:4:60)';
errCC = 0*n;
for k = 1:length(n)
    errCC(k) = exact - ccint(f,n(k));
end

figure(1)
semilogy( n, abs(errCC), '.-')
xlabel('number of nodes')
ylabel('error')
title('Spectral integration')
grid on

%%
% (The missing dots are where the error is exactly zero.)