Introduction
This page calculates the energy and power of the $ 2\sin(t)\cos(t) $ signal.
Power
$ P = \int_{t_1}^{t_2} \! |f(t)|^2\ dt $
$ P = \int_0^{2\pi} \! |2\sin(t)\cos(t)|^2\ dt $
$ P = \int_0^{2\pi} \! |sin(2t)|^2\ dt $
$ P = \int_0^{2\pi} \! sin^2(2t)\ dt $
$ P = \int_0^{2\pi} \! {(1-\cos(4t))\over 2} dt $
$ P = {1\over 2}\int_0^{2\pi} \! {(1-\cos(4t))} dt $
$ P = {1\over 2} ( t - {1\over 4}\sin(4t) )\mid_0^{2\pi} $
$ P = {1\over 2}t - {1\over 8}\sin(4t) \mid_0^{2\pi} $
$ P = {1\over 2}(2\pi) - {1\over 8}\sin(4*2\pi) - [{1\over 2}(0) - {1\over 8}\sin(4*0)] $
$ P = \pi - {1\over8}\sin(8\pi) $
$ P = \pi $
