Matlab Integration with syntax

I have a equation as x(t) = v * cos (θ(t)). I want its integration to use in matlab. How will be the syntax for that?

[Sumukh]

Can you elaborate on the integration of the equation and what has already been tried to do this?

[Torsten]

Use "integral" if theta(t) is known as an analytical expression:

https://uk.mathworks.com/help/matlab/ref/integral.html

Use "trapz" if you only have discrete values for theta(t):

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

Answer 1

[Jacob Mathew]

Hey Nasim,

Depending on nature of θ, you shall have to choose between the integral or the trapz function. If θ is being modelled as an analytical expression or a function, then use the integral function. However, if θ is a discrete value array or matrix, then use the trapz function.

Assuming that θ is an function of t, you can integrate it using the integral function by passing the function you are integrating as a function handle. Along with the function handle, you can pass the lower and upper limits of the integral to obtain the integrated output. Here is an example that does this:

% Define v and the function theta(t)
v = 1; % Example value, replace as needed
theta = @(t) t; % Example function, theta(t) = t

% Define the function to integrate
x = @(t) v * cos(theta(t));

% Define the integration limits
t_start = 0;
t_end = 10;

% Perform the integration
result = integral(x, t_start, t_end);

% Display the result
disp(['The integral of x(t) from ', num2str(t_start), ' to ', num2str(t_end), ' is: ', num2str(result)]);

The integral of x(t) from 0 to 10 is: -0.54402

You can reference the input argument section in the documentation of the integral function using the link below:

https://www.mathworks.com/help/releases/R2024b/matlab/ref/integral.html#btbbkta-3