The signal is: x(t) = 2cos(2t)
Energy
$ \int_0^{2\pi}{|2cos(2t)|^2dt} $
$ = 4 \times \frac{1}{2}\int_0^{2\pi}(1+cos(4t))dt $
$ =2 \times (t+\frac{1}{4}sin(4t))|_{t=0}^{t=2\pi} $
$ =2 \times (2\pi+\frac{1}{4}-0-0) $
$ =4*\pi + \frac{1}{2} $
Average Power
$ \frac{1}{2\pi - 0}\int_0^{2\pi}{|2cos(2t)|^2dt} $
$ =\frac{1}{2\pi} \times 4 \times \frac{1}{2}\int_0^{2\pi}(1+cos(4t))dt $
$ =\frac{1}{\pi} \times (t+\frac{1}{4}sin(4t))|_{t=0}^{t=2\pi} $
$ =\frac{1}{\pi} \times (2\pi+\frac{1}{4}-0-0) $
$ = 2 + \frac{1}{4\pi} $
