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\}=(1)/(s) \\ \\ L\{t^n\}=(n!)/(s^(n+1)) , \; \; \; n=1,\;2, \;3,...`

Applying the concept:

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