The Laplace transform of exp(at), where a 0, is defined only for the Laplace parameter, s a since______________?

Question

The Laplace transform of exp(at), where a > 0, is defined only for the Laplace parameter, s > a since______________?

Accepted Answer

The Laplace transform of integral of exp(at) has finite values only for s > a. The convergence of the Laplace transform integral requires that the integral of exp(at) remains finite. This condition leads to the requirement s > a.