Page 13 - LAPLACE TRANSFORM

1.2 Laplace Transform of a function by using Integration by parts

Integration by Parts is a special method of integration that is often useful when

two functions are multiplied together,

Integration by parts formula:

∫u v dx = u ∫v dx − ∫u' (∫v dx) dx

• u is the function u(x)
• v is the function v(x)

• u' is the derivative of the function u(x)

Example 2

Compute the following function f(t) using Laplace transform.

1. f (t) = 2 t

2
2. f (t) = 5 t

SOLUTION

∞
1. F(S) = ʆ {ƒ(t)} = ∫ ( ). − dt

∞
= ∫ 2 . − dt
0

7