Signal
$ y(t)=2cos(t) $
Energy
According to formula of Energy of a singal,we can get:
$ P = \int_{t_1}^{t_2} \! |f(t)|^2\ dt $
$ E=\int_0^{2\pi}{|2cos(t)|^2dt} $
$ =\int_0^{2\pi}{(2(2cos(t)^2-1)+2)dt} $
$ =\int_0^{2\pi}{2+cos(2t))dt} $
$ =(2t+sin(2t))|_{t=0}^{t=2\pi} $
$ =(4\pi+0-0-0) $
$ =(4\pi) $
Power
According to formula of Power of a singal,we can get: $ P = \frac{1}{2T}\int_{-T}^{T}\!|f(t)|^2\ dt $
$ = \frac{1}{4\pi}\int_{-2\pi}^{2\pi}\!|2\cos(t)|^2\ dt $
(comparing the integral part with Energy part, they are basically the same)
$ = \frac{1}{4\pi} $
$ = \frac{1}{4\pi}(4pi) $
$ = \pi $
