x(t) = sin t

Energy

$ E=\int_0^{2\pi}{|sin(t)|^2dt} $

$ =\frac{\int_0^{2\pi}(1-cos(2t))dt}{2} $

$ =\frac{t-\frac{1}{2}sin(2t)}{2}|_{t=0}^{t=2\pi} $

$ =\frac{1}{2}(2\pi-0-0+0) $

$ =\pi $

Power

$ P=\frac{1}{2\pi-0}\int_0^{2\pi}{|sin(t)|^2dt} $

$ P=\frac{1}{2\pi}E $

$ P=\frac{1}{2\pi}\pi $

$ P=\frac{1}{2} $

Alumni Liaison

Followed her dream after having raised her family.

Ruth Enoch, PhD Mathematics