Examples
Examples
Try the starting example
- Equally spaced sample values
- 0,1,4,9,16
- Spacing between sample x values
- 1
- Composite Simpson integral
- 21.333333
- Uniform subinterval count
- 4
- Total sampled x span
- 4
Try another scenario
- Equally spaced sample values
- 0,1,8,27,64
- Spacing between sample x values
- 1
- Composite Simpson integral
- 64
- Uniform subinterval count
- 4
- Total sampled x span
- 4
Calculation method
Calculation method
Composite Simpson integral
h/3 × [first+last+4×sum(odd interior indices)+2×sum(even interior indices)].
Uniform subinterval count
Sample count minus one, which must be even.
Total sampled x span
Spacing × subinterval count.
Symbols and units
- a
- Equally spaced sample values
- b
- Spacing between sample x values
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
sum(list) adds all entries in the list.
Assumptions & limits
Assumptions & limits
- Composite Simpson’s 1/3 rule for an odd count of at least three uniformly spaced samples. It cannot verify the spacing of an unlabelled list and gives no certified error estimate. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
SciPy: numerical integration and ODE method references ↗
Background reading; this does not imply endorsement or independent review of SumFizz.