Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral L{f(t)} L{f(t)} = [oe e-stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find £{f(t)}. (Write your answer as a function of s.) (5, f(t) 0, 0 ≤t<3 t≥ 3 (s > 0)

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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7.1.1

Use Definition 7.1.1.
DEFINITION 7.1.1 Laplace Transform
Let f be a function defined for t≥ 0. Then the integral
f(t)
L{f(t)} =
L{f(t)}:
=
is said to be the Laplace transform of f, provided that the integral converges.
Find £{f(t)}. (Write your answer as a function of s.)
15,
=
10,
f²e²
e-stf(t) dt
0 ≤t <3
t≥ 3
(s > 0)
Transcribed Image Text:Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral f(t) L{f(t)} = L{f(t)}: = is said to be the Laplace transform of f, provided that the integral converges. Find £{f(t)}. (Write your answer as a function of s.) 15, = 10, f²e² e-stf(t) dt 0 ≤t <3 t≥ 3 (s > 0)
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