Energy and Power calculation for $ x(t) = cos(2t) $ from $ 0 $ to $ 5 \pi $
Energy
$ E = \int_{0}^{5 \pi}{|cos(2t)|^2dt} $
$ = \int_{0}^{5 \pi}\frac{1 + cos(4t)}{2}dt $
$ =\frac{5 \pi}{2} + \frac{1}{8} sin(20 \pi) $
$ =\frac{5 \pi}{2} $
Power
$ P = \frac{1}{5 \pi - 0} \int_{0}^{5 \pi}{|cos(2t)|^2dt} $
$ = \frac{1}{5 \pi} \int_{0}^{5 \pi}\frac{[1 + cos(4t)]}{2}dt $
$ =\frac{1}{2} + \frac{1}{40 \pi} sin(20 \pi) $
$ =\frac{1}{2} $
