I've been learning Laplace Transform and I understand the method but I don't understand the boundary.
For example, Laplace transform on would be for . Why only for , I don't understand the boundary.
Then you know that the Laplace transform of f(x) is . In particular, the Laplace transform of f(x)= 1 is . If s were negative, that integral would not exist. For example, if s= -1, that integral is which would be and that limit does not exist.
Then you know that the Laplace transform of f(x) is . In particular, the Laplace transform of f(x)= 1 is . If s were negative, that integral would not exist. For example, if s= -1, that integral is which would be and that limit does not exist.
But that limit would work. It would just be ? Why is that wrong. It's not like we are getting an infinite answer.