Question

If f(t) = ^1 ⁄ √Πt, then its Laplace transform is?

(a) \(\frac{s^2-a^2}{(s-a)^2}\)

(b) S^-1/2

(c) \(\frac{n!}{(s-a)^{n-1}}\)

(d) \(\frac{n!}{(s-a)^{n-1}}\)

I have been asked this question in an online quiz.

Origin of the question is Existence and Laplace Transform of Elementary Functions in section Laplace Transform of Engineering Mathematics

Answer 1

Right choice is (b) S^-1/2

The best I can explain: The Laplace transform of a function is given by

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

put f(t) = 1 ⁄ √Πt

The solution for the above question is obtained by solving the above integral.