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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 interval can be $\mathbb{R} = ] -\infty ; +\infty [$ (the set R from minus infinity to plus infinity)

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

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

The primitive calculator is a also tool proposed on dCode.

## Source code

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