Project ForgeEngineering Mathematics
Calculus
GATE 2021
Medium
The Dirac-delta function δ(t-t₀) for t,t₀ ∈ ℝ has the property ∫ₐᵇ φ(t)δ(t-t₀)dt = φ(t₀) for a<t₀<b, and 0 otherwise. The Laplace transform of the Dirac-delta function δ(t-a) for a>0, L(δ(t-a)) = F(s), is
- A0
- B∞
- Ce^(sa)
- e^(-sa)
Explanation
L(δ(t-a)) = ∫₀^∞ e^(-st) δ(t-a) dt = e^(-sa), directly by the sifting property of the delta function (a>0 lies within the integration domain).
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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