Description
Return one moving-endpoint Leibniz boundary term.
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 one moving-endpoint Leibniz boundary term.
When to use this tool
Use Calculus: Leibniz Boundary Term when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter endpointValue, endpointSpeed, endpoint. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return one moving-endpoint Leibniz boundary term. Require endpoint upper or lower; boundaryTerm = endpointValue*endpointSpeed with positive upper and negative lower sign.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| endpointValue | Endpoint Value | Required. Finite number. |
| endpointSpeed | Endpoint Speed | Required. Finite number. |
| endpoint | Endpoint | Required. Text; one of "upper", "lower". Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned calculated value or nested object under the stated output convention. | Required. Object. |
| result.boundaryTerm | Boundary Term | Calculated result member: number. |
{
"input": {
"endpointValue": 3,
"endpointSpeed": 2,
"endpoint": "lower"
},
"output": {
"result": {
"boundaryTerm": -6
}
}
}Limitations and assumptions
- This omits the other endpoint and the integral of any parameter derivative of the integrand.
- Outputs are nested inside result. 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
- Integration Substitution Endpoint Order
Return mapped integration bounds and their orientation.
- Integral Subinterval Orientation
Apply endpoint orientation to a supplied ascending-order integral.