Mean value of a function. Hello friends, today it’s all about the mean 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 root mean square (rms) value of the function?**

**Mean value of a function**

The formula for the mean value of a function between and is

Now I’ll solve some examples of that.

**Solve examples of the mean value of a function**

Note: 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 mean height of the curve above the -axis between and .”

**Solution**

Now here the given equation of the curve is

And I have to find out its mean height above the -axis between and .

So as per the formula for the mean value of a curve,

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

Thus it gives

Then I’ll simplify it to get

Next, I’ll substitute the limits of integration. So becomes

Then I’ll simplify it to get

And that gives

Thus the mean height of the curve above the -axis between and 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), “Find the mean value of between and .”

**Solution**

Now here the given equation of the curve is

And I have to find its mean value between and .

So as per the formula for the mean value of a curve,

Now here I’ll use ‘integration by parts’ to integrate the function. According to the method of integration by parts,

So in this example, I’ll choose as and as .

Thus will be

Next, I’ll simplify it. So that gives

Then I’ll substitute the limits in the first part and integrate the second part to get

Now I’ll substitute the limits in the second part and simplify the first one to get

Next, I’ll simplify it. So that gives

Thus the mean value of between and is . 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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