fo (1) ((e-st) cos(1) ✓ ) at V dt 0 £{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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![The image presents a mathematical expression related to the Laplace Transform. The expression is:
\[ \mathcal{L}\{f(t)\} = \int_{0}^{\pi} \left( \left( e^{-st} \right) \cos(t) \right) \, dt \]
### Description:
- **\(\mathcal{L}\{f(t)\}\):** This denotes the Laplace Transform of the function \(f(t)\).
- **Integral:** The expression involves an integration from 0 to \(\pi\).
- **\(\left( e^{-st} \right)\):** This part of the expression is the exponential decay function, dependent on variables \(s\) and \(t\).
- **\(\cos(t)\):** This is the cosine function, representing periodic oscillation in terms of \(t\).
- **\(dt\):** This indicates integration with respect to the variable \(t\).
The expression is used in mathematical and engineering contexts to transform a given function into a form that can be more easily analyzed or solved, typically in the frequency domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74a50780-bdf2-45e2-b018-f4cc84bd693f%2Fe9d5d885-8324-4032-99c9-a54df5a4c6ff%2Fmwoa1av_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical expression related to the Laplace Transform. The expression is:
\[ \mathcal{L}\{f(t)\} = \int_{0}^{\pi} \left( \left( e^{-st} \right) \cos(t) \right) \, dt \]
### Description:
- **\(\mathcal{L}\{f(t)\}\):** This denotes the Laplace Transform of the function \(f(t)\).
- **Integral:** The expression involves an integration from 0 to \(\pi\).
- **\(\left( e^{-st} \right)\):** This part of the expression is the exponential decay function, dependent on variables \(s\) and \(t\).
- **\(\cos(t)\):** This is the cosine function, representing periodic oscillation in terms of \(t\).
- **\(dt\):** This indicates integration with respect to the variable \(t\).
The expression is used in mathematical and engineering contexts to transform a given function into a form that can be more easily analyzed or solved, typically in the frequency domain.
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