How to write exponential function with limits?

Hi, How can I write the following two functions

Can I use "piece wise" function? If yes than how to use it?

[Rik]

Do you want a symbolic function, or an anonymous function?

[rohail khan]

Actually I have a RC circuit with some values.I just want to use the above function in the following equation to solve the circuit.

Answer 1

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/391290-how-can-i-write-this-exponential-function-in-matlab I showed you g(x) already. You can use the same technique for U

[rohail khan]

thanks Walter. So can I write the function as :

   u = @(t) 0 .* (x <= 0) + sin(100*pi*t).*(x>0)

[Walter Roberson]

Yes, but you can shorten that to

u = @(t) sin(100*pi*t) .* (x>=0);

[Walter Roberson]

RC = 0.04;
U = @(t) sin(100*pi*t) .* (t >= 0);
F = @(s, t) exp(-s./RC) .* U(t-s);
X = @(t) integral(@(s) F(s,t), 0, inf) ./ RC;
Xv = @(t) arrayfun(X, t);

fplot(Xv, [-1 1])

[rohail khan]

wow thats amazing.Its working.I spend the whole day yesterday but couldnt solve it.Thank you sooooooooo much Walter