How can I integrate a vector that varies as a function of length of time?

t=2:201;

s=1:200;

mu = [10*ones(1,length(t)/4) 15*ones(1,length(t)/4) 20*ones(1,length(t)/4) 10*ones(1,length(t)/4)] ;

for i =1:length(t)

p= integeral(mu,s(i),t(i))

end

I am a beginner to matlab and wanted to find the integeral of the vector mu. can any one help me please? Mu fanction is assigned 10 for the first 50 intervals, 15,20 and 10 for the conscative 50 intervals each.

Thank you!

Answer 1

[Rushil]

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”.

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:

https://mathworks.com/help/matlab/ref/trapz.html

Hope it helps