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Mean of a Function

Tool to compute the mean of a function in order to find the average value of its integral over a given interval.

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Mean of a Function -

Tag(s) : Mathematics

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Mean of a Function

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Mean of a Function Calculator






Tool to compute the mean of a function in order to find the average value of its integral over a given interval.

Answers to Questions

How to compute the average value of a function?

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 using 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 \( f(x) \).

Example: Consider the function \( f(x) = x \), the mean over the interval \( [0;1] \) is calculated like this: $$ F(x) = \frac{1}{2} x^2 \\ \bar{f} = \frac{1}{1-0} \int^1_0 f(x) \mathrm{ dx} = F(1)-F(0) = \frac{1}{2} $$

The integration calculation used in the mean function calculator uses the primitive calculator also proposed on dCode.

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