Description
Multiply rightX - leftX by the mean of endpoint y values for integral, requiring increasing x.
Linear interpolation blends endpoint values by a normalized coordinate. Its value weights, inverse slope, and sensitivities to moving nodes answer different questions and use different units.
Multiply rightX - leftX by the mean of endpoint y values for integral, requiring increasing x.
When to use this tool
Use Linear Interpolant Integral One Cell when you need one explicitly defined linear interpolation term.
How to use the tool and how it works
- Enter leftX, rightX, leftY, rightY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read integral. Use the output convention below.
Multiply rightX - leftX by the mean of endpoint y values for integral, requiring increasing x.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftX | Left X | Required. Finite number. |
| rightX | Right X | Required. Finite number. |
| leftY | Left Y | Required. Finite number. |
| rightY | Right Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| integral | Integral | Required. Finite number. |
{
"input": {
"leftX": 1,
"rightX": 4,
"leftY": 2,
"rightY": 6
},
"output": {
"integral": 12
}
}Limitations and assumptions
- The result is the exact integral of the linear interpolant, not necessarily of the underlying unknown function.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate endpoints and units and use a complete evaluator when clamping, extrapolation, or uncertainty propagation is required.
References
Similar or alternative tools
- Linear Interpolant Node Value Sensitivity
Return 1 - t and t as sensitivities to the left and right node values.
- Affine Knot Parameter
Require left different from right and return (knot - left)/(right - left) as parameter.