Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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 \( f(t) \).
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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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