6. Laplace Transforms of Integrals

We first saw the following properties in the Table of Laplace Transforms.


1. If G(s) = laplace{g(t)}, then MATH


2. For the general integral, if

MATH

is the value of the integral when t = 0, then:

MATH

 


EXAMPLES

Use the above information and the Table of Laplace Transforms to find the Laplace transforms of the following integrals:

(a) MATH $dt$


Answer


(b) MATH $dt$


Answer


(c) MATH $dt$


Answer


(d) integral sin at cos at


Answer





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