For a Continuous Time Signal
Energy from $ t_{1} $ to $ t_{2} $
$ E = \int_{t_1}^{t_2}\!|x(t)|^2\ dt $
$ E = \int_{t_1}^{t_2}\!|\sqrt{t}|^2\ dt $
$ E = \int_{t_1}^{t_2}\!t\ dt $
$ E = \frac{1}{2}t^{2}|^{t_{2}}_{t_{1}} $
$ E = \frac{1}{2}(t^{2}_{2}-t^{2}_{1}) $
Average power in time interval from [$ t_{1},t_{2} $]:
$ P_{avg} = \frac{1}{{t_2}-{t_1}}\int_{t_1}^{t_2}\!|x(t)|^2\ dt $
$ P_{avg} = \frac{1}{{t_2}-{t_1}}\int_{t_1}^{t_2}\!|\sqrt{t}|^2\ dt $
$ P_{avg} = \frac{1}{{t_2}-{t_1}}\int_{t_1}^{t_2}\!t\ dt $
$ P_{avg} = \frac{1}{{t_2}-{t_1}}(\frac{1}{2}t^{2}|^{t_{2}}_{t_{1}}) $
$ P_{avg} = \frac{1}{{t_2}-{t_1}}(\frac{1}{2}(t^{2}_{2}-t^{2}_{1})) $
