Page 11 - LAPLACE TRANSFORM

Example 3

Find Laplace Transform, of the following by using the Definition

of Laplace Transform.

f ( t) = e t 2

∞
F( s) = ∫ e − st • e t 2 dt

0

= ∫ ∞ e −t ( −2s ) dt
ο

 e − st ( −2 )  ∞
=  − (s − )2 
 1  ο 

= 0 + (s − ) 

2


= 1 where s > a
s − 2

Example 4

4