Learn How to Calculate RMS and Avoid Mistakes: Root Mean Square Help

[coki2000]

Hello,
For 1 and 2 I want to calculate rms then

$$x_{rms}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_i^2}\Rightarrow x_{1,2}=\sqrt{\frac{1}{2}(1^2+2^2)}=\sqrt{\frac{5}{2}}$$

And also

$$x_{rms}=\sqrt{\frac{1}{x_2-x_1}\int_{x_1}^{x_2}f^2(x)dx}$$

For the function $$f(x)=x$$, $$x_1=1$$, $$x_2=2$$

$$x_{rms}=\sqrt{\frac{1}{2-1}\int_{1}^{2}x^2dx}=\sqrt{\frac{7}{3}}$$

Please explain to me where I do wrong.
Thanks

 

[elibj123]

You do nothing wrong
Are you expecting to get the same value?
Well you won't because the discrete set {1,2} is different from the continuous set {x | 1<x<2}, therefore you shouldn't get the same value

 

[coki2000]

You do nothing wrong
Are you expecting to get the same value?
Well you won't because the discrete set {1,2} is different from the continuous set {x | 1<x<2}, therefore you shouldn't get the same value

Alright how I write this integral form?Thanks.