Discuss is there a solution or not (why) of Laplace transformation of L(frac{1}{t})

ka1leE 2021-01-13 Answered
Discuss is there a solution or not (why) of Laplace transformation of
L(1t)
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Expert Answer

Tuthornt
Answered 2021-01-14 Author has 107 answers
Step 1
The Laplace transform of the function f(t) is defined by the integral:
L(f,s)=0estf(t)dt
for those s where the integral converges
Step 2
First find the Laplace transform for the value of f(t)=1t
L(f,s)=0estf(t)dt
f(t)=1t
L(1t,s)=0est1tdt
Put st=x and sdt=dx
0exsx1sdx=0ex(dx)x
0e(x)(dx)x01ex(dx)x>e101(dx)x
e1[ln(x)]01( Does not exist )
Step 3
Hence, L(1t) does not exist.
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