Find the Laplace transform for (a) and (b). a) b) c) Verify the results obtained in (a)
Chapter 12, Problem 12.24(choose chapter or problem)
Find the Laplace transform for (a) and (b).
a) \(f(t)=\frac{d}{d t}\left(e^{-a t} \cos \omega t\right)\).
b) \(f(t)=\int_{0^{-}}^{t} e^{-a x} \sin \omega x \ d x\).
c) Verify the results obtained in (a) and (b) by first carrying out the indicated mathematical operation and then finding the Laplace transform.
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