Question

If f(t) = te^-at, then its Laplace transform is?

(a) \(\frac{1}{(s+a)^2}\)

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

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

(d) Indeterminate

I have been asked this question in a national level competition.

I need to ask this question from Existence and Laplace Transform of Elementary Functions in division Laplace Transform of Engineering Mathematics

Answer 1

The correct answer is (a) \(\frac{1}{(s+a)^2}\)

Easiest 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) = te^-at

On solving, the required answer is obtained.