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
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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.
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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