Laplace Transformation On Integral Function

Laplace Transformation on Integral Function-1:

2. Laplace Transforms of the form tⁿ f (t) where n is a positive integer:

In this section we shall find the Laplce Transforms of the functions of the form tⁿ f (t) where n is a positive integer if the laplace transform of f (t) is known.

Theroem:

Proof: We shall prove the theorem for n = 1.

Differentiate w.r.t 's' we get;

In the RHS we shall apply Lebnitz rule for the differentiation under the integral sign,

By repeated this process of the above theorem, we get;