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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].

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Mean of a Function -

Tag(s) : Functions

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# 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 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 !

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