Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral 00 L{f(t)} = e-stf(t) dt s said to be the Laplace transform of f, provided that the in f(t) = lo, J cos(t), 0 ≤t<π † Σπ Complete the integral(s) that defines L{f(t)}. π L{f(t)} = f ( dt + [(
Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral 00 L{f(t)} = e-stf(t) dt s said to be the Laplace transform of f, provided that the in f(t) = lo, J cos(t), 0 ≤t<π † Σπ Complete the integral(s) that defines L{f(t)}. π L{f(t)} = f ( dt + [(
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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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
L{f(t)} = [0
e-stf(t) dt
is said to be the Laplace transform of f, provided that the integral converges.
0 ≤ t < π
f(t)
J cos(t),
10,
† Σπ
Complete the integral(s) that defines L{f(t)}.
I
L{f(t)}
dt +
=
+ L (
dt
Find L{f(t)}. (Write your answer as a function of s.)
L{f(t)} :
(s > 0)
=
=
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