Question

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

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

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

(c) \(\frac{\Gamma(p+1)}{s^{p+1}}\)

(d) 1/s^2

I got this question in final exam.

This intriguing question comes from Existence and Laplace Transform of Elementary Functions in portion Laplace Transform of Engineering Mathematics

Answer 1

Right answer is (d) 1/s^2

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) = t to solve the problem.