2. Laplace Transform of an Integral and a Derivative (a) Consider the function, f(t) = So exp(-37) cos(27)dr. Without integrating, determine the Laplace transform of f(t). (b) Consider the funtion, f(t) = t(d/dt)[exp(-t) cos(t)]. Without carrying out the differ- entiation, determine the Laplace transform of f(t).
2. Laplace Transform of an Integral and a Derivative (a) Consider the function, f(t) = So exp(-37) cos(27)dr. Without integrating, determine the Laplace transform of f(t). (b) Consider the funtion, f(t) = t(d/dt)[exp(-t) cos(t)]. Without carrying out the differ- entiation, determine the Laplace transform of f(t).
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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![2. Laplace Transform of an Integral and a Derivative
(a) Consider the function, \( f(t) = \int_{0}^{t} \exp(-3\tau) \cos(2\tau) \,d\tau \). Without integrating, determine the Laplace transform of \( f(t) \).
(b) Consider the function, \( f(t) = t \left( \frac{d}{dt} \right) [\exp(-t) \cos(t)] \). Without carrying out the differentiation, determine the Laplace transform of \( f(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfe453bd-e2eb-4e43-9db0-ee551a10fd19%2Fe49a0b64-6bd1-444d-ab8d-ff440488b373%2Fjvqtr5i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Laplace Transform of an Integral and a Derivative
(a) Consider the function, \( f(t) = \int_{0}^{t} \exp(-3\tau) \cos(2\tau) \,d\tau \). Without integrating, determine the Laplace transform of \( f(t) \).
(b) Consider the function, \( f(t) = t \left( \frac{d}{dt} \right) [\exp(-t) \cos(t)] \). Without carrying out the differentiation, determine the Laplace transform of \( f(t) \).
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