Hello
I believe that the task of integration over a piecewise constant function can be accomplished using the “trapz” function.
For each interval defined by 
and 
, you can compute the integral by selecting the corresponding segment from the mu function and applying “trapz”.
and , you can compute the integral by selecting the corresponding segment from the mu function and applying “trapz”. In this approach, s and t are selected to remain within the bounds of mu, thereby preventing indexing errors.
Refer to the below given code snippet for better understanding:
t = 2:200;
s = 1:199;
mu = [10*ones(1,50) 15*ones(1,50) 20*ones(1,50) 10*ones(1,50)];
integral_mu = zeros(1, length(t));
for i = 1:length(t)
segment = mu(s(i):t(i));
% trapz for numerical integration
integral_mu(i) = trapz(s(i):t(i), segment);
end
% plot the results
plot(s, integral_mu)
xlabel('s')
ylabel('Integral of mu from s to t')
title('Numerical Integral of mu')
You may read more about “trapz” at the link below:
Hope it helps
