Question

If f(t) = t^p where p > – 1, its Laplace Transform is given by?

(a) √π ⁄ 2√s

(b) f(t) = tsin(at)

(c) γ(p+1) ⁄ s^p+1

(d) Does not exist

This question was addressed to me in class test.

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

Answer 1

The correct answer is (d) Does not exist

Easy explanation: 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^p

On Solving, we get γ(p+1) ⁄ s^p+1.