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Riemann Sums — result sheet
Left, right, and trapezoidal sums from evenly spaced heights.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: n = m-1; h = (b-a)/n; left/right/trapezoid weightings of heights.
Width comes from the interval split into height-count minus one parts. Left drops the last height, right drops the first, trapezoid halves the ends.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Heights — At least 2 comma-separated values, evenly spaced.
- Left endpoint a — minimum -1000000000000; maximum 1000000000000
- Right endpoint b — Must exceed a.; minimum -1000000000000; maximum 1000000000000
- Rule — 3 choices
Worked example
| Input | Value |
|---|---|
| Heights | 0, 1, 4 |
| Left endpoint a | 0 |
| Right endpoint b | 2 |
| Rule | left |
Left 1; right 5; trapezoid 3.
Assumptions and limits
- At least 2 finite heights, evenly spaced over [a, b].
- Right endpoint b exceeds left endpoint a.
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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