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R0006-03836 · q-20261007-advance-20261009-r06-definite-integral-0086
On all R, the constant integrand is c=11≠0. Starting at a=-2, its oriented integral has target 242/2. Recover b, which is promised to remain an integer endpoint in this slice. Use reduced positive-denominator fractions, retaining /1 for integers.
G001 — On all R, the constant integrand is c=11≠0. Starting at a=-2, its oriented integral has target 242/2. Recover b, which is promised to remain an integer endpoint in this slice. Use reduced positive-denominator fractions, retaining /1 for integers.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
explicit real polynomial moment or constant integrand model
After
oriented I(a,b)=H(b)−H(a);do not sort endpoints
Conditions: none
Real polynomials are continuous and integrable;use termwise primitive endpoint differences for exact oriented integrals,not absolute area or a finite sum.
Rule: polynomial_moment_scope · Uses: G001
Before
oriented interval displacement := div(121, 11)
After
oriented interval displacement = 11
Conditions: none
Divide c(b−a)=target by nonzero c,without absolute values.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
recovered endpoint := sum(-2, 11)
After
recovered endpoint = 9
Conditions: none
Add the oriented displacement to a;this frozen exercise slice requires an integer endpoint.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
endpoint reverse substitution := mul(11, 11)
After
endpoint reverse substitution = 121
Conditions: none
Substitute into c(b−a) to audit the target;target0 gives b=a.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
c=11≠0;b=9
After
I(a,b)=121=target
Conditions: none
A nonzero constant makes the endpoint unique;negative c or target does not permit arbitrary endpoint reordering.
Rule: unique_constant_endpoint · Uses: G001, S004
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Recompute endpoint reverse substitution with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute recovered endpoint with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute oriented interval displacement with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.9/1
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
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