If we assume that then Use this result to find the Laplace

Chapter 7, Problem 66E

(choose chapter or problem)

If we assume that \(\mathscr{L}\{f(t) / t\}\) exists and \(\mathscr{L}\{f(t)\}=F(s)\), then

\(\mathscr{L}\left\{\frac{f(t)}{t}\right\}=\int_{s}^{\infty} F(u) d u\).

Use this result to find the Laplace transform of the given function. The symbols a and k are positive constants.

(a) \(f(t)=\frac{\sin a t}{t}\)

(b) \(f(t)=\frac{2(1-\cos k t)}{t}\)

Text Transcription:

mathscr L f(t) / t

mathscr L ft=F(s)

mathscr L {f(t)/t}=int_s^infty F(u) d u

f(t)=sin a t/t

f(t)=2(1-cos k t)/t