How to define an integral function of a piecewise function

Hello!

I want to define an integral function but I have a problem with the integral function. This is my code:

syms s t
figure(1)
P = [0.5 1.25 2 4.5 5 7.25];
for i=1:4 
        subplot(4,2,i)
        hold on
        a = @(s) (s-P(i))/(P(i+1)-P(i)); 
        b = @(s) (P(i+2)-s)/(P(i+2)-P(i+1));
        
        f(i) = piecewise(s<=P(i),0, P(i)<s<=P(i+1),a(s), P(i+1)<s<=P(i+2),b(s), s>P(i+2),0);
        fplot (f(i),[0,P(4)])
        hold off
        grid
        
        subplot(4,2,i+1)
        hold on
        F = @(t) integral(f(i), 0, t);
        fplot(F(t),[0,P(4)])
        hold off
        grid
end

In particular, there is no problem with the function f, however Matlab returns the following error:

Error using integral (line 82)
First input argument must be a function handle.
Error in example_f_int>@(t)integral(f(i),0,t) (line 19)
        F = @(t) integral(f(i), 0, t);
Error in example_f_int (line 20)
        fplot(F(t),[0,P(4)])

There is a way to solve this error and finaly plot the F funciont?

Thanks, any help would be appreciated!

Answer 1

[Abhisek Pradhan]

Intergral function take a function handle as its first argument. Adding @(arg) Infront of piecewise () may work.

Refer the following link for more details on how to use integral function.

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

[Chiara Boetti]

Hi!

As you suggest, I've changed the code with

f = @(s,i) piecewise(s<=P(i),0, P(i)<s<=P(i+1),a(s), P(i+1)<s<=P(i+2),b(s), s>P(i+2),0);
fplot (f(s,i),[0,P(4)])

and

F = @(t) integral(f(s,i), 0, t);

However there is still an error:

Error using integral (line 82)
First input argument must be a function handle.

Error in example_f_int>@(t)integral(f(s,i),0,t) (line 17)
        F = @(t) integral(f(s,i), 0, t);

Error in example_f_int (line 18)
        fplot(F(t),[0,P(4)])

What did I do wrong?

Thanks