The Dirac-delta function (δ(t - t 0 )) for t, t 0 ∈ R, has the following property \int _{a}^{b}\phi (t)\delta(t−t_{0})dt = {\\begin{array}{c}\phi (t_{0\end{array}) , a < t_{0} < b ; \text{ 0} , \text{otherwise} ; }. The Laplace transform of the Dirac-delta function δ(t - a) for a > 0; L(\delta (t−a)) = F(s) is

GATE Mechanical Engineering (ME) 2021 Shift 1 Solved Paper

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The Dirac-delta function (δ(t - t₀)) for t, t₀ ∈ R, has the following property

∫ _{a}^{b}φ (t)δ(t−t_{0})dt = {\{\table φ (t_{0}) , a < t_{0} < b ; \text" 0" , \;\text "otherwise"\; ; }.

The Laplace transform of the Dirac-delta function δ(t - a) for a > 0;

L(δ (t−a)) = F(s)

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