Search for a tool
Mean of a Function

Tool to compute the mean of a function (continuous) in order to find the average value of its integral over a given interval [a,b].

Results

Mean of a Function -

Tag(s) : Functions

Share dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Mean of a Function tool. Thank you.

# Mean of a Function

## Average of a Function Calculator

### Upper bound

Tool to compute the mean of a function (continuous) in order to find the average value of its integral over a given interval [a,b].

### How to compute the average value of a function?

The mean of a function $f$ is noted $\bar{f}$ and is calculated over an interval $[a,b]$ with the formula $$\bar{f}=\frac{1}{b-a}\int_a^bf(x)\,dx$$ with $$\int^b_a f(x) \mathrm{ dx} = F(b)-F(a)$$ with $F(x)$ the primitive of $f(x)$ over the interval $[a,b]$

Example: Calculate the mean of the function $f(x) = x$ over the interval $[0;1]$ necessitate to calculate the primitive $F(x) = \frac{1}{2} x^2$ and then $$\bar{f} = \frac{1}{1-0} \int^1_0 f(x) \mathrm{ dx} = F(1)-F(0) = \frac{1}{2}$$

### How to compute the average value of a function with dCode?

Indicate the function with lower and upper bounds (that delimitate the interval) and the variable to integrate with.

Symbolic values are allowed and included in the calculation.

dCode will compute the integral of the function and will find the average value.

The function must be continuous (without asymptotes) to obtain results

### How to calculate the primitive of a function?

The primitive calculator is a also tool proposed on dCode.

## Source code

dCode retains ownership of the source code of the script Mean of a Function online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Mean of a Function script for offline use on PC, iPhone or Android, ask for price quote on contact page !