For example, suppose we have the following two problems that we'd like to find the Laplace transform of:
$f(t) = \begin{cases} 1, & t \lt 2 \\ 0, & t \geq 2 \end{cases}$
$f(t) = \begin{cases} 1-0.5t, & t \lt 2 \\ 5, & t \geq 2 \end{cases}$
Is there a general method to solve these sorts of problems? How can I approach them and make solving them more intuitive?
Thanks for the help!