Find the laplace transform by definition. a) L{2}, b)L{e^(2t)}, c)L[3^(-3t)]

Cheyanne Leigh 2021-03-06 Answered

Find the laplace transform by definition.
a) L{2}
b) L{e2t}
c) L[e3t]

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Expert Answer

Nola Robson
Answered 2021-03-07 Author has 94 answers
Step 1
Here we finding the Laplace transform of given function by the definition . We perform the definite integral as definition :
Step 2
Answer: By the definition Laplace transform of f(t) is given as:
L{f(t)}=0estf(t)dt
a) f(t)=2
L{2}=0est2dt=20estdt
=2[ests]0=2[es+e0ss]=2[0+1s]=21s
L{2}=2s
b) L{e2t}=0este2tdt=0e(2s)tdt
=[e(2s)t2s]0=[e(2s)e(2s)02s]=[012s]
=12s=1s2L{e2t}=1s2
c) L{e3t}=0este3tdt=0e(s+3)tdt
=[e(s+3)ts+3]0=[e(s+3)e(s+3)0s+3]=[0+1s+3]
L{e3t}=1s+3
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