What is the average value of atlernating current, `I = I_(0) sin omega t` over time interval `t = pi//omega` to `t = pi//omega` ?

Explanation

To find the average value of the alternating current given by the equation \( I = I_0 \sin(\omega t) \) over the time interval \( t = \frac{\pi}{\omega} \) to \( t = \frac{2\pi}{\omega} \), we can follow these steps:

### Step 1: Identify the Time Interval
The time interval given is from \( t = \frac{\pi}{\omega} \) to \( t = \frac{2\pi}{\omega} \). This corresponds to half of the complete cycle of the sine wave, as the full cycle (period \( T \)) is \( T = \frac{2\pi}{\omega} \).

### Step 2: Set Up the Average Value Formula
The average value \( I_{\text{avg}} \) of a function over a time interval \( [t_1, t_2] \) is given by the formula:
\[
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