Page 14 - LAPLACE TRANSFORM
P. 14
By using Integration by parts formula:
−1
−1
= (t) ( e ) − ꭍ (1) ( e ) dt ;0 < t < ∞
-s t
-s t
−1
1
-s t
-s t
= (t) ( e ) + ꭍ (e ) dt ;0 < t < ∞
−1 1 1 ∞
-s t
= (t) ( e ) + ( ) [ − ]
− 0
1 1 ∞
= 0 − ( ) [ − ]
0
1
= 0 − [ 0 − 1 ]
2
1 1 1
= − [ −1 ] = = [ ]
2 2 2
2
F(S) =
2
Laplace Transform Table
3 Linear t
8
