Page 10 - LAPLACE TRANSFORM

Example 1

Find Laplace Transform, of the following by using the Definition of
Laplace Transform

ƒ( t ) = a
(sF ) = ∫ ο ∞ e − st f . ( ) dtt

(sF ) = ∫ ο ∞ e −st (a) dt

e −st  ∞
= a  
 − s  ο
 e −∞  e 0  
= a  −  



 − s  − s  
  1   1  a
= a 0 −   = a   = where s > a


  −   s  s  s

Example 2

Find Laplace Transform, of the following by using the Definition of Laplace

Transform

f (t ) = 7

∞
−
st
F( s) = ∫ e ( ) 7 dt
0

e −st  ∞
= 7  
 − s  ο

 e −∞  e 0  
= 7  −  



 − s  − s  
  1   7
= 7  0 −   = 7  1  = where s > a


  −   s  s  s

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