Question

Determine the Laplace Transform of {t sin√2t}​

Answer 1

Step-by-step explanation:

L{∫t0f(τ)dτ}=1sF(s)L{∫0tf(τ)dτ}=1sF(s)

Let L{sint√}=F(s).L{sin⁡t}=F(s).

I used Wolfram Alpha to solve the integral:

∫t0sin(τ−−√)dτ=2sin(t√)−2t√cos(t√)∫0tsin⁡(τ)dτ=2sin⁡(t)−2tcos⁡(t)

So, based on the above theorem we have:

L{2sin(t√)−2t√cos(t√)}=1sF(s)L{2sin⁡(t)−2tcos⁡(t)}=1sF(s)

This seems to be the most appropriate answer.

hope it will help you

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