clear
format compact

%%
% This function gets increasingly oscillatory near the right endpoint.
f = @(x) (x+1).^2.*cos((2*x+1)./(x-4.3));
fplot(f, [0 4], 2000)
xlabel('x')
ylabel('f(x)')
title('A wiggly integrand')
grid on

%%
% Accordingly, the trapezoid rule is more accurate on the left half of the
% interval than on the right half.
n_ = 50*2.^(0:3)';
T_ = [];
for i = 1:length(n_)
    n = n_(i);
    T_(i,1) = trapezoid(f,0,2,n); 
    T_(i,2) = trapezoid(f,2,4,n);
end

left_val = integral(f,0,2,'abstol',1e-14,'reltol',1e-14);
right_val = integral(f,2,4,'abstol',1e-14,'reltol',1e-14);
table(n_,T_(:,1)-left_val,T_(:,2)-right_val,... 
    'variablenames',{'n','left_error','right_error'})

%%
% Both the picture and the numbers suggest that more nodes should be used
% on the right half of the interval than on the left half.