# Average Value of a Function Calculator

The word average refers to the mean of a value. In the average value of the function, we apply definite integrals y = f (x) over a specific interval, i.e., (a, b). In order to get the average value, we apply the Fundamental Theron of Calculus.

The average value of a function is represented as fave.

## Formula of Average Value of a Function Calculator

We use the below-mentioned formula to get the exact average value of the function:

$\mathop f\nolimits_{avg} = \frac{1}{{b - a}}\int\limits_a^b {f(x)dx}$

Where,

a = 1st value

b = 2nd value

x = function

Note:

### Example

We have the function, f(x) = x2 + x + 1 on the interval (1,3)

Putting values in the formula:

$\mathop f\nolimits_{avg}= \frac{1}{{b - a}}\int\limits_a^b {f(x)dx}$ $\mathop f\nolimits_{avg} = \frac{1}{{1 - 3}}\int\limits_1^3 {f(\mathop x\nolimits^2 + x + 1)dx}$

$\mathop f\nolimits_{avg} = \frac{1}{2}\left[ {\frac{{{x^3}}}{3} + \frac{{{x^2}}}{2} + \mathop {\left. x \right|}\nolimits_1^3 } \right]$

$\mathop f\nolimits_{avg} = \frac{1}{2}\left[ {\left( {\frac{{9 + 9}}{{2 + 3}}} \right) - \left( {\frac{1}{3} + \frac{1}{2} + 1} \right)} \right]$ $\mathop f\nolimits_{avg} = \frac{1}{2}\left[ {11 + 4 - \frac{1}{3}} \right]$ $\mathop f\nolimits_{avg} = \frac{1}{2}\left[ {\frac{{45}}{3} + \frac{1}{3}} \right]$ $\mathop f\nolimits_{avg} = \frac{1}{2}\left[ {\frac{{44}}{3}} \right]$ $\mathop f\nolimits_{avg} = \frac{{22}}{3}$

The average value of the function f(x) = x2 + x + 1 is 22/3.

### How to use Average Value of a Function Calculator?

The steps to use the average value of a function calculator are as follows:

Step 1: Enter the values separated by a comma in the first required input.

Step 2: The calculator will automatically display an answer on the screen.

### Calculator use

By using the average value of the function calculator, you can determine the value by clicking a button merely. Forget the complex calculations now and get your answers by putting the functions and intervals at a time.