Question

Use theorem 7.1.1 to find {f(t)}. (write your answer as a function of s.) f(t) = t2 + 5t − 6 {f(t)} =

Answer 1

f(s) = (2s)/(s^3) + 5/(s^2) - 6/s

Answer 2

General Idea:

Let $f$ be a function defined for $t\geq 0$. Then the integral

$L\{f(t)\}=\int\limits^\infty_0 {e^{-st}f(t)} \, dt$

is said to be Laplace transform of $f$, provided that the integral converges.

$L\{1\}=\frac{1}{s} \\ \\ L\{t^n\}=\frac{n!}{s^{n+1}} , \; \; \; n=1,\;2, \;3,...$

Applying the concept:

$L\{f(t)\}=L\{t^2\}+L\{5t\}-L\{6\}=\frac{2}{s^3} +\frac{5}{s^2} -\frac{6}{s}$