Question:
The RMS value of \(x^2\) in \([0,1]\) is
The RMS value of \(x^2\) in \([0,1]\) is
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RMS means square the function, take mean value, then square root.
Updated On: May 7, 2026
- \(\frac{1}{\sqrt5}\)
- \(\frac{1}{5}\)
- \(\frac{1}{\sqrt3}\)
- \(\frac{1}{3}\)
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The Correct Option is A
Solution and Explanation
Step 1: RMS value of \(f(x)\) in \([a,b]\) is: \[ \sqrt{\frac{1}{b-a}\int_a^b [f(x)]^2\,dx} \]
Step 2: Here, \[ f(x)=x^2,\qquad a=0,\qquad b=1 \]
Step 3: \[ \text{RMS}=\sqrt{\int_0^1 x^4\,dx} \]
Step 4: \[ =\sqrt{\left[\frac{x^5}{5}\right]_0^1} \] \[ =\sqrt{\frac{1}{5}} \] \[ =\frac{1}{\sqrt5} \] \[ \boxed{\frac{1}{\sqrt5}} \]
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