Description
Return mapped integration bounds and their orientation.
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 mapped integration bounds and their orientation.
When to use this tool
Use Integration Substitution Endpoint Order when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter mappedLower, mappedUpper. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read orientation, lower, upper. Use the output convention below.
Return mapped integration bounds and their orientation. orientation = sign(mappedUpper-mappedLower), lower/upper sort the mapped endpoints.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mappedLower | Mapped Lower | Required. Finite number. |
| mappedUpper | Mapped Upper | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| orientation | Orientation | Required. Safe integer. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
{
"input": {
"mappedLower": 5,
"mappedUpper": 2
},
"output": {
"orientation": -1,
"lower": 2,
"upper": 5
}
}Limitations and assumptions
- This is endpoint bookkeeping only; the substitution derivative, monotonicity and integral transformation are not checked.
- 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 Subinterval Orientation
Apply endpoint orientation to a supplied ascending-order integral.
- Calculus: Leibniz Boundary Term
Return one moving-endpoint Leibniz boundary term.