Q.Define average value of an alternating current.

Why not a full-cycle average. A symmetric sinusoidal AC current has equal, opposite-signed positive and negative half-cycles, so its average over one COMPLETE cycle is always exactly zero -- useless for characterising the waveform's typical magnitude.

Definition and derivation. The average (mean) value of AC is instead defined as the average of all its values over just ONE half-cycle (positive or negative). For $i=I_m\sin\theta$, integrating over the positive half-cycle ($0$ to $\pi$) gives area $\int_0^{\pi}I_m\sin\theta\,d\theta = I_m[-\cos\theta]_0^{\pi} = 2I_m$; dividing by the half-cycle base length $\pi$ gives

and, by the same symmetry, $I_{av}=-0.637I_m$ over the negative half-cycle. The identical relation holds for average voltage, $V_{av}\approx0.637V_m$. …