Question

If f(t) = t^n ⁄ n, then its Laplace transform is?

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

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

(c) \(\frac{2a^3}{(s^2+a^2)}\)

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

I got this question in a job interview.

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

Answer 1

Right answer is (d) \(\frac{(n-1)!}{s^{n+1}}\)

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

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

put f(t) = t^n ⁄ n

On solving, we obtain the Laplace transform of the required function.