Question

Find the Laplace Transform of f(t) = t^2, I have no idea what Laplace Transform is, but it's in the homework, a short definition is given though: integral [inf,0] f(t)e^(-st) dt

Answer 1

Let me explain to u a bit what Laplace transform mean? well basically its a migration from one world to another world in an exponential transport way...

Answer 2

now let me solve the problem for u then i will explain what is this all about, this is a very important topic

Answer 3

by definition ...
\[\int\limits_{0}^{\infty} f(t)e^{=st}dt\]

Answer 4

\[f(t)=t^2\]

Answer 5

\[\int\limits\limits_{0}^{\infty} t^2e^{=st}dt\]

Answer 6

now when u have two functions multiplied by each other we apply something called integration by parts right!

Answer 7

so let u=t^2, v'=e^{-st}, u'=2t,and v=-(1/s)e-{st}

Answer 8

Oh..So just solve this using integration by parts? This question is confusing me b/c there is a hint
Hint: Use can use without proof (although
the proof would just require L'Hopital's Rule) that for all real numbers n,
\[\lim_{z \rightarrow \infty} z^n e^{-sz} = 0\]

Answer 9

yes exactly

Answer 10

the limit is there to help u solve the problem of undefined integral limits...

Answer 11

This question seems hard but in fact it's not, anyways, thx a lot :)

Answer 12

ur welcome...

Answer 13

u may also use the table of laplace transform

Answer 14

L{t^2}=2!/s^3