how to calculate error using repeat simpsons rule in matlab

main.m
err = (1/15) * abs(S2n - Sn)
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main.m
% function to be integrated
f = @(x) x.*sin(x);

% limits of integration
a = 0;
b = pi;

% number of intervals
n = 4;

% repeated Simpson's rule
h = (b - a) / (2 * n);
x = a:h:b;
S = (h / 3) * (f(x(1)) + 4*f(x(2)) + f(x(3)));
for i = 2:n
    xi = a + (2*i - 2) * h;
    S = S + (h / 3) * (f(xi) + 4*f(xi + h) + f(xi + 2*h));
end
fprintf('Approximated value of integral using repeated Simpson''s rule: %.6f\n',S);

% error
h = (b - a) / (2 * (n+1));
x = a:h:b;
Sn = (h / 3) * (f(x(1)) + 4*f(x(2)) + f(x(3)));
for i = 2:n+1
    xi = a + (2*i - 2) * h;
    Sn = Sn + (h / 3) * (f(xi) + 4*f(xi + h) + f(xi + 2*h));
end
err = (1/15) * abs(S2n - Sn);
fprintf('Error in using repeated Simpson''s rule: %.6f\n',err);
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