Use Definition 7.1.1.DEFINITION 7.1.1 Laplace TransformLet f be a function defined for t 2 0. Then the integralLMt)} = | e-str(t) dtis 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.)[7, 0st< 5f(t) =0,t2 5L{f(t)} = ||(s > 0)

L{7} Use Laplace Transform table: L{a}=a/s L{7}=7/s =7/s

Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral LRt)} = | 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.) S7, [7, 0st< 5 f(t) 10, t2 5 L{f(t)} = | (s > 0)

Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral LRt)} = | 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.) S7, [7, 0st< 5 f(t) 10, t2 5 L{f(t)} = | (s > 0)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use Definition 7.1.1.
DEFINITION 7.1.1 Laplace Transform
Let f be a function defined for t 2 0. Then the integral
LMt)} = | e-str(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.)
[7, 0st< 5
f(t) =
0,
t2 5
L{f(t)} = ||
(s > 0)

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