Signal Energy
The signal energy expanded from $ t_1\! $ to $ t_2\! $ is defined as $ E = \int_{t_1}^{t_2} \! |f(t)|^2\ dt $.
The following is an example problem to find the signal energy for $ x(t)=e^{2t}\! $ on $ [0,2]\! $:
$ E = \int_{0}^{2} |e^{2t}|^2\ dt \! $
$ = \int_{0}^{2} e^{4t}\ dt \! $
$ = (1/4)[e^{4t}]_{t=0}^{t=2} \! $
$ = (1/4)(e^8 -1)\! $
