Chapter 7.1, Problem 37P

Given $a>0$, let $f\left(t\right)=1$ if $0\underset{\_}{\underset{\_}{<}}1<a,f\left(t\right)=0$ if $t\underset{\_}{\underset{\_}{>}}a$. First, sketch the graph of the function f, making clear its value at t = a. Then express f in terms of unit step functions to show that ${L}\left\{f\left(t\right)\right\}=s^{-1}\left(1-e^{-as}\right)$ .