Description
Calculate the trapezoid-minus-left-rectangle correction from supplied endpoints.
Local calculus terms distinguish derivative components, signed interval widths, endpoint values and correction terms. A trapezoid correction is not the whole integral, and agreement of supplied derivatives does not prove differentiability. Scalar operations preserve the chosen direction and approximation rather than assessing the function globally.
Calculate the trapezoid-minus-left-rectangle correction from supplied endpoints.
When to use this tool
Use Endpoint Trapezoid Correction Term when you already have intervalWidth, leftValue, rightValue and need to calculate the trapezoid-minus-left-rectangle correction from supplied endpoints.
How to use the tool and how it works
- Enter intervalWidth, leftValue, rightValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read correctionToLeftRectangle. Use the output convention below.
Return intervalWidth*((rightValue-leftValue)/2).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| intervalWidth | Interval Width | Required. Finite number. |
| leftValue | Left Value | Required. Finite number. |
| rightValue | Right Value | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| correctionToLeftRectangle | intervalWidth*(rightValue-leftValue)/2; correction only, not the full trapezoidal integral. | Required. Finite number. |
{
"input": {
"intervalWidth": 2,
"leftValue": 3,
"rightValue": 5
},
"output": {
"correctionToLeftRectangle": 2
}
}Limitations and assumptions
- Signed widths and values are accepted. This is a correction term, not the full trapezoid integral, derivative estimate, error bound or actual function evaluation.
- 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
Use the full function, derivative or quadrature method for the mathematical problem. Check smoothness, interval orientation and approximation error separately; local supplied-value terms do not establish those conditions.
References
Similar or alternative tools
- Local Integral Rectangle Correction
Compare a supplied local integral with a left-rectangle term.
- One Sided Derivative Agreement Residual
Compare supplied right and left derivative values.