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Area Between Two Curves (Simpson) — result sheet
Approximates area between sampled top and bottom curves with one Simpson panel.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: d = top − bottom; area = (b − a)/6 × (d0 + 4d1 + d2).
Differences the sampled heights, then weights the midpoint fourfold. One panel suits smooth gaps; jagged curves need more panels.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Top values (start, mid, end) — Exactly 3 numbers, evenly spaced.
- Bottom values (start, mid, end) — Exactly 3 numbers, same spacing as top.
- Lower limit a — minimum -1000000000; maximum 1000000000
- Upper limit b — Must exceed a.; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Top values (start, mid, end) | 0, 1, 4 |
| Bottom values (start, mid, end) | 0, 0, 1 |
| Lower limit a | 0 |
| Upper limit b | 2 |
Area ≈ 2.3333.
Assumptions and limits
- Three samples sit at a, the midpoint, and b in order.
- Top stays at or above bottom over [a, b].
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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