L{f;je*sin(t- t)dr}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Find the Laplace Transform. Given solution: 1/(s-1) * 1/(s^2+1)
![The image displays the following mathematical expression:
\[ \mathcal{L} \left\{ \int_{0}^{t} e^{\tau} \sin(t - \tau) \, d\tau \right\}. \]
This expression represents the Laplace transform of the integral of the function \( e^{\tau} \sin(t - \tau) \) with respect to \( \tau \) over the interval from 0 to \( t \).
- \(\mathcal{L}\{\}\) denotes the Laplace transform operator.
- \(\int_{0}^{t}\) signifies the definite integral from 0 to \( t \).
- \( e^{\tau} \) and \(\sin(t - \tau)\) are the exponential and sine functions, respectively, as part of the integrand.
This type of expression is often encountered in the analysis of linear time-invariant systems and differential equations. It involves both convolution and transformation techniques, which are fundamental concepts in engineering and applied mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64800780-3a27-40b8-a11a-6cbcd87af243%2F32018f9f-b489-4796-ad6d-80ab605f7d87%2Fdwpldj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays the following mathematical expression:
\[ \mathcal{L} \left\{ \int_{0}^{t} e^{\tau} \sin(t - \tau) \, d\tau \right\}. \]
This expression represents the Laplace transform of the integral of the function \( e^{\tau} \sin(t - \tau) \) with respect to \( \tau \) over the interval from 0 to \( t \).
- \(\mathcal{L}\{\}\) denotes the Laplace transform operator.
- \(\int_{0}^{t}\) signifies the definite integral from 0 to \( t \).
- \( e^{\tau} \) and \(\sin(t - \tau)\) are the exponential and sine functions, respectively, as part of the integrand.
This type of expression is often encountered in the analysis of linear time-invariant systems and differential equations. It involves both convolution and transformation techniques, which are fundamental concepts in engineering and applied mathematics.
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