Techniques of Integration · Hard problem

Two generators feed the same resistor, so the total current is $i(t)=3\sin(\omega t)+4\cos(\omega t)$ amps. With resistance $R=2\;\Omega$, the average power dissipated over one full period is $P_{\text{avg}}=\dfrac{1}{T}\displaystyle\int_0^T R\,i(t)^2\,dt$. Find $P_{\text{avg}}$ (in watts).