Solving Physics Integral: V^2_\textrm{rms}

AI Thread Summary
The discussion focuses on the challenge of solving the integral for the root mean square voltage, V^2_\textrm{rms}, given by the formula V^2_\textrm{rms}=\frac{1}{T}\int_{0}^{T}V^2_0sin^2(2ft\pi)dt. Users are struggling to obtain a sensible answer, often resulting in incorrect values like 0 or V_0. A suggestion is made to use the identity cos(2θ) = 1 - 2sin²(θ) to simplify the integral, with the frequency f defined as 1/T. The conversation highlights the need for clarity in handling the squared terms under the integral sign. Overall, the thread emphasizes the complexities involved in solving the integral for V^2_\textrm{rms}.
tmc
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I have this formula, and I just can't seem to be able to find any sensible answer:

V^2_\textrm{rms}=\frac{1}{T}\int_{0}^{T}V^2_0sin^2(2ft\pi)dt

Depending on what I do, I either get an obviously wrong answer, 0, or V_0.
 
Last edited:
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The stuff under the integral sign needs to be squared. This is the S part of rms.

Regards,
George
 
yeah, my bad. Edited it.
Still don't get how to solve it though.
 
Use cos(2\theta) = 1 - 2sin^2 (\theta) and f = 1/T.

Regards,
George
 

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