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GATE ME 2021 Set 1 — Question 13

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MCQ+1 / -0.33EasyLaplace Transforms & ApplicationsDifferential EquationsEngineering Mathematics

Engineering Mathematics → Differential Equations → Laplace Transforms & Applications

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Question

The Dirac-delta function (δ(t−t0)\delta(t - t_0)) for t,t0∈Rt, t_0 \in \mathbb{R}, has the following property∫abϕ(t)δ(t−t0)dt={ϕ(t0)a<t0<b0otherwise\int_a^b \phi(t)\delta(t - t_0)dt = \begin{cases} \phi(t_0) & a < t_0 < b \\ 0 & \text{otherwise} \end{cases}The Laplace transform of the Dirac-delta function δ(t−a)\delta(t - a) for a>0a > 0; L(δ(t−a))=F(s)\mathcal{L}(\delta(t - a)) = F(s) is
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