DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral L{f(t)} = ™ e-stf(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. (Write your answer as a function of s.) f(t) L{f(t)} = = Submit Answer t, 0≤ t < 1 t≥ 1 1, (s > 0)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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)
is said to be the Laplace transform of f, provided that the integral converges.
Find L{f(t)}. (Write your answer as a function of s.)
L{f(t)} =
=
L{f(t)} =
Submit Answer
fore e-stf(t) dt
t, 0≤ t < 1
1,
t≥ 1
(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) is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. (Write your answer as a function of s.) L{f(t)} = = L{f(t)} = Submit Answer fore e-stf(t) dt t, 0≤ t < 1 1, t≥ 1 (s > 0)
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