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Controlled Rectifier Bridge

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Good Day Experts,

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
However, I have also tried integrating to find the RMS value and used the limits
\[0 \to \ \pi\]
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.
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