I need your help in regards to the controlled rectifier bridge circuit below:

I need help calculating the RMS value of the fundamental component of source current. The electrical circuit is a fully controlled single phase rectifier bridge. In the lecture the value is

\[Is_{1}=\frac{2\sqrt{2}}{\pi}I_{0}\]

However, I have also tried integrating to find the RMS value and used the limits

\[0 \to \ \pi\]

\[I_{RMS}=\frac{I_{0}}{\sqrt{2}}\]

Then, I tried integrating from

\[\alpha \to (\pi + \alpha )\]

I got the following:

\[I_{RMS}=\frac{I_{0}}{\sqrt{2 \pi}}\]

All of the values I got are different than the one shown in the lecture. Please make any suggestions and point me in the right direction. Don't hesitate to provide corrections.