# Prove rms voltage using integration

1. Dec 27, 2009

### iamnew

1. The problem statement, all variables and given/known data

ac voltage
v=sinx

2. Relevant equations

how do you prove that rms voltage is 0.707v using integration

3. The attempt at a solution

2. Dec 27, 2009

### Fightfish

The root-mean-square value of a function is the root of the average of the square of the function.
The average of the square of a function f (x) over an interval is given by:
$$\frac{\int_{t_{1}}^{t_{2}} (f (x))^{2} dx}{t_{2} - t_{1}}$$​
You can do the relevant integration yourself for f (x) = sin x (or any sinusoidal function for that matter)