The instantaneous power output P(t)P(t)P(t) of a specific alternating current component, measured in Watts, is modeled by the function:
P(t)=(3sin2t+5cos2t)2 P(t) = (3\sin 2t + 5\cos 2t)^2 P(t)=(3sin2t+5cos2t)2where ttt is the time in seconds. The total energy E(t)E(t)E(t) transferred by the component is given by E(t)=∫P(t) dtE(t) = \int P(t) \, dtE(t)=∫P(t)dt.
Determine the general expression for E(t)E(t)E(t) in its simplest form.
