Question

If f(t) = t^n where, ‘n’ is an integer greater than zero, then its Laplace Transform is given by?

(a) n!

(b) t^n+1

(c) n! ⁄ s^n+1

(d) Does not exist

I had been asked this question in an online interview.

The question is from Existence and Laplace Transform of Elementary Functions in section Laplace Transform of Engineering Mathematics

Answer 1

Correct option is (c) n! ⁄ s^n+1

The best I can explain: The Laplace Transform of a functions is given by

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

f(t) = t^n

On simplifying, we get n! ⁄ s^n+1.