Question

Laplace transform question.Given we know f^(n)(p)* = Integral from 0 to infinity of (e^-(ps)(-s)^(n)f(s)ds)

How would we use this to compute f(p) of x^(n)e^(ax)?

*ie where f has been differentiated n times

Answer 1

\[f ^{n}(p)=\int\limits_{0}^{infinity}e^{-ps}(-s)^{n}f(s)ds\]

If this helps visualise the problem

Answer 2

We seek \[L[x ^{n}e ^{ax};p] \] which we know is \[\frac{ n! }{(p-a)^{n+1} }\] but how do we get there? using our given information?

Answer 3

First plug in the value of f(x) that you have been given in the formula for n derivative of f(p) But if you need f(p) then use