Find the Laplace transformation (evaluating the improper integral that defines this transformation) of the real valued function f(t) of the real varia

chillywilly12a 2021-03-04 Answered
Find the Laplace transformation (evaluating the improper integral that defines this transformation) of the real valued function f(t) of the real variable t>0. (Assume the parameter s appearing in the Laplace transformation, as a real variable).
f(t)=2t24cosh(3t)+et2
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Expert Answer

Alara Mccarthy
Answered 2021-03-05 Author has 85 answers

Step 1

here f(t)=2t24cosh(3t)+et2
we know that
L{tn}=n!sn+1,L{cosh(at)}=ss2a2
L{et2}=F(s2)12iπes24
Also , L{f(t)+g(t)+h(t)}=L{f(t)}+L{g(t)}+L{h(t)}
Taking Laplace transform of eq
L{f(t)}=L{2t24cosh(3t)+et2}
=2L{t2}4L{cosh(3t)}+L{et2}
=22!s2+14ss232+F(s2)12iπes24
L{f(t)}=4s34ss29+F(s2)12iπes24
Step 2
This is required Laplace transformation of given f(t).

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