Elementary mathematical derivation method of sinusoidal alternating current RMS

If you don't understand, you can only use calculus to prove it. If you want to know how to prove calculus, you can help me

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1. Why is the RMS of sinusoidal alternating current equal to twice the root of the peak?
2. I don't know if it's right that I use calculus to deduce the effective value of sine alternating current I use calculus to deduce the voltage and current RMS of sinusoidal alternating current. I don't know if the process is correct
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11. What is the derivation formula of sinusoidal AC RMS? Such as the title
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