Example 12.8.  Show that  ,  where a is a real constant.

Explore Solution 12.8.

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  .

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

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