Average Value Of A Function Calculator
Work out average value of a function instantly with clear inputs, formula shown and shareable results.
About Average Value Of A Function Calculator
The average value of a continuous function is its integral divided by the interval width — the height of the rectangle with the same area. The mean value theorem for integrals guarantees the function actually attains it somewhere.
Formula
Average value
f̄ = (1/(b − a)) ∫ₐᵇ f(x) dx
Worked example
With the default values below, Average Value Of A Function Calculator returns Average value of 4.33333333. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Polynomial coefficients, highest power first
- 1, 0, 0
- From x =
- 1
- To x =
- 3
Results
- Average value
- 4.33333333
- Definite integral
- 8.66666667
- Interval width
- 2.000000
- Point where the function equals its average
- 2.082000
Step by step
- 1Values used
- 2Average value
- 3Average value= 4.33333333
- 4Definite integral= 8.66666667
- 5Interval width= 2.000000
- 6Point where the function equals its average= 2.082000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Average of x² on [0, 3]?
The integral is 9, divided by 3 gives 3, attained at x = √3 ≈ 1.7320508.
Is this the same as averaging sample values?
It is the limit of that process as the samples become infinitely dense and evenly spaced.