Description
Compare a supplied local integral with a left-rectangle term.
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.
Compare a supplied local integral with a left-rectangle term.
When to use this tool
Use Local Integral Rectangle Correction when you already have intervalWidth, leftValue, suppliedIntegral and need to compare a supplied local integral with a left-rectangle term.
How to use the tool and how it works
- Enter intervalWidth, leftValue, suppliedIntegral. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftRectangle, integralMinusRectangle. Use the output convention below.
Return intervalWidth*leftValue and suppliedIntegral-that product.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| intervalWidth | Signed integration width; a negative width reverses the local contribution. | Required. Finite number. |
| leftValue | Left Value | Required. Finite number. |
| suppliedIntegral | Supplied Integral | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftRectangle | Left Rectangle | Required. Finite number. |
| integralMinusRectangle | Integral Minus Rectangle | Required. Finite number. |
{
"input": {
"intervalWidth": 2,
"leftValue": 3,
"suppliedIntegral": 8
},
"output": {
"leftRectangle": 6,
"integralMinusRectangle": 2
}
}Limitations and assumptions
- Signed widths and values are accepted. No function, integral, approximation error bound or complete quadrature is calculated or verified.
- 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
- Endpoint Trapezoid Correction Term
Calculate the trapezoid-minus-left-rectangle correction from supplied endpoints.
- Derivative Unit Ratio Label
Qualify an explicit derivative unit-ratio record by order text.