Page 10 - LAPLACE TRANSFORM
P. 10
1.1 Laplace Transform of a function by using the Integration
definition
Definition
The Laplace transform of ƒ(t) is denoted ʆ {ƒ(t)} and defined as;
∞ −
F(S) = ʆ {ƒ(t)} = ∫ ( ) ; 0 < t < ∞
0
Example 1
Evaluate the following integral using Laplace transform.
1. f (t) = 10
2. f (t) = A
–at
3. f (t) = e
at
4. f (t) = e
SOLUTION
∞ −
1. F(S) = ʆ {ƒ(t)} = ∫ . f(t) dt
∞
= ∫ − . (10) dt
0
∞
= (10) ∫ − dt
0
∞
= (10) ( ) [ − ]
− 0
= ( ) [ − (∞) − − (0) ]
−
4
