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].
Mean of a Function - dCode
Tag(s) : Functions
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!
Mean of a Function
Average of a Function Calculator
Answers to Questions (FAQ)
What is the average value of a function? (Definition)
The mean of a function $ f $ is noted $ \bar{f} $ and is calculated over an interval $ [a,b] $ with the formula $$ \bar{f} = \frac{1}{b-a} \int_a^b f(x) \mathrm{ dx} $$ 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] $
How to compute the average value of a function?
Calculate the integral of the function over the desired interval and divide by the size of the interval.
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 and convergent 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 "Mean of a Function" source code. Except explicit open source licence (indicated Creative Commons / free), the "Mean of a Function" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Mean of a Function" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Mean of a Function" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Mean of a Function" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Mean of a Function on dCode.fr [online website], retrieved on 2024-11-05,
