Question

If f(t) = δ(t), then its Laplace transform is?

(a) s + a ⁄ (s – a)^2 + b^2

(b) a^3 ⁄ (s^2 + a^2)^2

(c) 1

(d) Does not exist

This question was addressed to me in class test.

The doubt is from Existence and Laplace Transform of Elementary Functions topic in chapter Laplace Transform of Engineering Mathematics

Answer 1

Right option is (c) 1

Easiest explanation: The Laplace transform of a function is given by

\(\{f(t)\}=F(s)=\int_0^{\infty} f(t)e^{-st}dt\)

put f(t) = δ(t)

Solve the above integral to obtain 1 as RHS.