Example 12.11.   Show that  .  

Explore Solution 12.11.

Method 1.  Enter the function    and compute the integral defining   .  

Assuming that f(t) is of exponential order, we have  . Then  ,  and the Laplace transform can be computed by the calculation  .

Method 2.  Since  ,  we can use  .  

Aside. We can check this with Mathematica's  result using the LaplaceTransform package.

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