Theorem 12.14  (Integration of f(t) ).  Let [Graphics:Images/LaplaceDiffIntegrateMod_gr_27.gif] be continuous for [Graphics:Images/LaplaceDiffIntegrateMod_gr_28.gif], and of exponential order and [Graphics:Images/LaplaceDiffIntegrateMod_gr_29.gif], then  

            [Graphics:Images/LaplaceDiffIntegrateMod_gr_30.gif].

Proof.

Proof of Theorem 12.14.

Proof of Theorem 12.14 is in the book.

Complex Analysis for Mathematics and Engineering

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell