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Simpson's 1/3 Rule Integral — result sheet
Approximates a definite integral from endpoint and midpoint values with one Simpson panel.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: (b−a)/6 × (f(a) + 4f(mid) + f(b)).
Fits a parabola through the three points and integrates it exactly. One panel suits smooth curves over a short interval.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- f(a) — minimum -1000000000000; maximum 1000000000000
- f(mid) — Value at the midpoint (a+b)/2.; minimum -1000000000000; maximum 1000000000000
- f(b) — minimum -1000000000000; maximum 1000000000000
- Lower limit a — minimum -1000000000000; maximum 1000000000000
- Upper limit b — Must be greater than a.; minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| f(a) | 0 |
| f(mid) | 2 |
| f(b) | 0 |
| Lower limit a | 0 |
| Upper limit b | 2 |
Integral ≈ 2.6667.
Assumptions and limits
- f is smooth on [a, b]; sharp spikes need more panels.
- Single panel with b > a; uneven or wide intervals lose accuracy.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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