(Solved): Use Definition 7.1.1. Definition 7.1.1 Laplace Transform \[ f(t)=\left\{\begin{array}{ll} 6, & 0 \ ...

Use Definition 7.1.1. Definition 7.1.1 Laplace Transform \[ f(t)=\left\{\begin{array}{ll} 6, & 0 \leq t<4 \\ 0, & t \geq 4 \end{array}\right. \] Complete the integral(s) that defines \( \mathscr{L}\{f(t)\} \). \[ \mathscr{L}\{f(t)\}=\int_{0}\left(d t+\int^{\infty}(1) d t\right. \] Find \( \mathscr{L}\{f(t)\} \). (Write your answer as a function of s.)