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
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!


Please, check our community Discord for help requests!


Thanks to your feedback and relevant comments, dCode has developped the best Mean of a Function tool, so feel free to write! Thank you !

Mean of a Function

Sponsored ads

Average of a Function Calculator




Lower bound



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].

Answers to Questions

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 online 'Mean of a Function' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) no data, script or API access will be for free, same for Mean of a Function download for offline use on PC, tablet, iPhone or Android !

Need Help ?

Please, check our community Discord for help requests!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developped the best Mean of a Function tool, so feel free to write! Thank you !


Source : https://www.dcode.fr/mean-function
© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback