DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral L{f(t)} provided that the integral converges. Consider the following function. L{f(t)} = f(t) 1 1 (3, 6) = - fºe- e-stf(t) dt is said to be the Laplace transform of f, 0 Use Definition 7.1.1, to find L{f(t)}. (Write your answer as a function of s.) (s > 0)

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DIFFERENTIAL EQUATION

DEFINITION 7.1.1 Laplace Transform
Let f be a function defined for t > 0. Then the integral L{f(t)}
provided that the integral converges.
Consider the following function.
L{f(t)} =
f(t)
1
1
(3, 6)
=
- fºe-
e-stf(t) dt is said to be the Laplace transform of f,
0
Use Definition 7.1.1, to find L{f(t)}. (Write your answer as a function of s.)
(s > 0)
Transcribed Image Text:DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral L{f(t)} provided that the integral converges. Consider the following function. L{f(t)} = f(t) 1 1 (3, 6) = - fºe- e-stf(t) dt is said to be the Laplace transform of f, 0 Use Definition 7.1.1, to find L{f(t)}. (Write your answer as a function of s.) (s > 0)
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