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2 { ["² 28. L sin 7 cos(t 7)dT -

2 { ["² 28. L sin 7 cos(t 7)dT -

Advanced Engineering Mathematics
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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Question
Evaluate the Laplace transform by using the convolution Theron
**28.** \(\mathcal{L} \left\{ \int_0^t \sin \tau \cos(t - \tau) \, d\tau \right\}\) This expression involves taking the Laplace transform, denoted by \(\mathcal{L}\), of an integral with bounds from 0 to \(t\). The integrand is the product of \(\sin \tau\) and \(\cos(t - \tau)\), where \(\tau\) is the variable of integration. The objective is to analyze and transform this integral within the context of Laplace transforms, which are frequently utilized for solving differential equations and system analysis in engineering and physics.
Transcribed Image Text:**28.** \(\mathcal{L} \left\{ \int_0^t \sin \tau \cos(t - \tau) \, d\tau \right\}\) This expression involves taking the Laplace transform, denoted by \(\mathcal{L}\), of an integral with bounds from 0 to \(t\). The integrand is the product of \(\sin \tau\) and \(\cos(t - \tau)\), where \(\tau\) is the variable of integration. The objective is to analyze and transform this integral within the context of Laplace transforms, which are frequently utilized for solving differential equations and system analysis in engineering and physics.
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