Root mean square value of a function. Hello friends, today I’ll talk about the root mean square (rms) value of a function. Have a look!!

Want to know more about the mean value of a function? Do check out:

**How to get the mean value of a function**

**Root mean square value of a function**

Suppose is the equation of a curve. Then the root mean square (rms) value of the function between ad will be

Now I’ll give some examples of that.

**Solved examples of the root mean square value of a function **

Disclaimer: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

**Example 1**

According to Stroud and Booth (2013)*, “Find the rms value of over the range to .”

**Solution**

Now here the given function is . And I have to find its rms value over the range to . Thus it will be

And that means

So this gives

Now I’ll integrate it using the * standard formulas in integration*. And that means

Next, I’ll substitute the limits to get

Then I’ll simplify it. And that gives

Therefore the rms value of the function is

Hence I can conclude that this is the answer to the given example.

Now I’ll give another example.

**Example 2**

According to Stroud and Booth (2013)*, “Calculate the rms value of between and .”

**Solution**

Now here the given function is . And I have to get its rms values between and . Thus it will be

And that means

So this gives

Then I’ll integrate it to get

Next, I’ll substitute the limits to get

Then I’ll simplify it. So that gives

And this is because .

Now I’ll simplify it a bit more to get the value of as

So I can rewrite it as

And that means

Therefore the rms value of the function will be

Hence I can conclude that this is the answer to the given example.

Dear friends, this is the end of today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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