Question

(ii). Find inverse Laplace transform of
1
2/3
(
8-9)​

Answer 1

In Section 8.1 we defined the Laplace transform of  f  by

F(s)=L(f)=∫∞0e−stf(t)dt.

We’ll also say that  f  is an inverse Laplace Transform of  F , and write

f=L−1(F).

To solve differential equations with the Laplace transform, we must be able to obtain  f  from its transform  F . There’s a formula for doing this, but we can’t use it because it requires the theory of functions of a complex variable. Fortunately, we can use the table of Laplace transforms to find inverse transforms that we’ll need.