Description
Check power-tail integrability at infinity.
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.
Check power-tail integrability at infinity.
When to use this tool
Use Improper Tail Power Integrability when evaluating the stated integral contribution, orientation, Jacobian or convergence condition.
How to use the tool and how it works
- Enter power. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read integrable, logarithmicBoundary. Inspect integrable, logarithmicBoundary before interpreting the associated values.
Check power-tail integrability at infinity. integrable means power < -1, logarithmicBoundary means power === -1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| power | Power | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| integrable | Integrable | Required. Boolean. |
| logarithmicBoundary | Logarithmic Boundary | Required. Boolean. |
{
"input": {
"power": -2
},
"output": {
"integrable": true,
"logarithmicBoundary": false
}
}Limitations and assumptions
- This assumes a nonzero constant multiple of x^power on a positive tail away from zero; other factors and the finite endpoint are not analyzed.
- 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
- Endpoint Singularity Integrability Power
Check local power integrability near a finite endpoint.
- Definite Integral Calculator
Approximate a finite real expression integral with 256-panel composite Simpson quadrature; the refinement error estimate assumes a smooth integrand and is not a certified bound or improper integral solver.