Determine the Laplace transform of f{{left({t}right)}}={t}^{4}-{t}^{2}{e}^{{{3}{t}}}+{2}

sanuluy 2020-12-24 Answered
Determine the Laplace transform of
f(t)=t4t2e3t+2
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Expert Answer

yunitsiL
Answered 2020-12-25 Author has 108 answers

Step 1
The given function is f(t)=t4t2e3t+2
Find the Laplace transform of f(t)=t4t2e3t+2 as shown below.
Step 2
It is known that,
L{1}=1s
L{tn}=n!sn+1
(L{t(at)}=n!(sa)n+1
Then,
L{f(t)}=L{t4t2e3t+2}
=L{t4}L{t2e3t}+L{2}=L{t4}L{t2e3t}+2L{1}
=24s52(s3)3+2s

Step 3
Therefore, the Laplace transform of the function f(t)=t4t2e3t+2  is  L{f(t)}=24s52(s3)3+2s

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