Question

If f(t)=√t, then its Laplace Transform is given by?

(a) ^1⁄2

(b) ^1⁄s

(c) √π ⁄ 2√s

(d) Does not exist

The question was asked during a job interview.

This interesting question is from Existence and Laplace Transform of Elementary Functions in division Laplace Transform of Engineering Mathematics

Answer 1

The correct choice is (c) √π ⁄ 2√s

To explain I would say: The Laplace Transform of a functions is given by

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

Put f(t)=√t

On Solving, we get √π ⁄ 2√s.