Description
Return moving-integral endpoint contributions.
Integration depends on the domain, orientation, coordinate change and endpoint behavior. A boundary contribution, Jacobian factor or power-tail test is a local part of an integral calculation; convergence, a valid change of variables and the complete integral require their own hypotheses.
Return moving-integral endpoint contributions.
When to use this tool
Use Integral Moving Bound Normal Sign when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter lowerValue, lowerVelocity, upperValue, upperVelocity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lowerTerm, upperTerm, derivative. Use the output convention below.
Return moving-integral endpoint contributions. lowerTerm = -lowerValue*lowerVelocity, upperTerm = upperValue*upperVelocity, derivative sums both.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lowerValue | Lower Value | Required. Finite number. |
| lowerVelocity | Lower Velocity | Required. Finite number. |
| upperValue | Upper Value | Required. Finite number. |
| upperVelocity | Upper Velocity | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lowerTerm | Lower Term | Required. Finite number. |
| upperTerm | Upper Term | Required. Finite number. |
| derivative | Derivative | Required. Finite number. |
{
"input": {
"lowerValue": 2,
"lowerVelocity": 3,
"upperValue": 4,
"upperVelocity": 5
},
"output": {
"lowerTerm": -6,
"upperTerm": 20,
"derivative": 14
}
}Limitations and assumptions
- This includes only boundary motion and omits any integral of explicit parameter dependence of the integrand.
- 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
Specify and analyze the complete integrand and domain, including endpoint singularities, coordinate invertibility and any omitted boundary or interior terms.
References
Similar or alternative tools
- Integral Orientation Composition Sign
Compose supplied orientation signs.
- Integral Subinterval Orientation
Apply endpoint orientation to a supplied ascending-order integral.