Let f be a function defined for t≥ 0. Then the integral is said to be the Laplace transform of f, provided that the integral converges. f(t) = {-1 0 st < 1 t21 Complete the integral(s) that defines L{f(t)}. X Dat+ f Find L{f(t)}. (Write your answer as a function of s.) (s > 0) L{f(t)} = 00 £{f(t)} = "* e¯stf(t) dt L{f(t)} 10 dt

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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
is said to be the Laplace transform of f, provided that the integral converges.
f(t) = { 1,
L{f(t)} =
00
L{f(t)} = e-stf(t) dt
Complete the integral(s) that defines L{f(t)}.
+ f
L{f(t)} =
10
0 < t < 1
t≥ 1
dt+
Find L{f(t)}. (Write your answer as a function of s.)
(s > 0)
dt
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 is said to be the Laplace transform of f, provided that the integral converges. f(t) = { 1, L{f(t)} = 00 L{f(t)} = e-stf(t) dt Complete the integral(s) that defines L{f(t)}. + f L{f(t)} = 10 0 < t < 1 t≥ 1 dt+ Find L{f(t)}. (Write your answer as a function of s.) (s > 0) dt
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