MATLAB symbolic definite integration error while taking symbolic function as input arguments

The code is

syms v T;
int(@(x) x*v, 0, T)
int(@(tau) tau*v, 0, T)

I expect the answers to be but the second definite integration incorrectly contains τ.

Answer 1

[Sameer]

Hi @Noah Tang

In the code you have provided, you are trying to perform symbolic integration using anonymous functions, which isn't directly compatible with MATLAB's "symbolic math" capabilities.

Here's a revised version of your code:

syms v T x tau;

% First integral
integrand1 = x * v;
result1 = int(integrand1, x, 0, T);

% Second integral
integrand2 = tau * v;
result2 = int(integrand2, tau, 0, T);

disp('Result of the first integral:');
disp(result1);

disp('Result of the second integral:');
disp(result2);

Hope this helps!

[Noah Tang]

Thanks for your quick response! I now understand the difference between a symbolic function, which can be used as an input argument for the int function, and an anonymous function that involves a symbolic expression. Thanks again!

Answer 2

[Walter Roberson]

syms a v T
disp(int(@(tau) tau*v, 0, T))
disp(int(@(tau) tau*a, 0, T))

Notice that in the first case, it integrated with respect to v and kept tau constant, but in the second case it integrated with respect to tau and kept a constant.

What is happening is the anonymous function is being automatically converted to a symbolic expression (not a symfun !), and then the symbolic expression is being integrated with respect to the default variable. The default variable happens to be different between [tau, v] and [tau, a]

It is arguably a bug. On the other hand, no behaviour is documented for int() of anonymous functions.

[Walter Roberson]

I submitted a case about this.