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.
Table of Contents
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:
To know about the isosceles triangle, visit our Isosceles Triangle Calculator.
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.
