Laplace Transform of Constant Mapping/Examples

Examples of Laplace Transform of Constant Mapping

Example $1$

Let $\map f t$ be the real function defined as:

$\forall t \in \R: \map f t = \begin {cases} 0 & : t < 0 \\ 5 & : 0 \le t < 3 \\ 0 & : t \ge 3 \end {cases}$

Then the Laplace transform of $f$ is given by:

$\laptrans {\map f t} = \dfrac {5 \paren {1 - e^{-3 s} } } s$