Question 1377: Antiderivative Value Retaining the Actual Constant

Original question and givens

On all R, f has ascending coefficients [0], starting with its constant term. Let F0 be its zero-constant primitive. Find F0(3)+(1), retaining the actual additive constant. Give a reduced fraction with positive denominator, retaining /1 for integers.

• G001 — On all R, f has ascending coefficients [0], starting with its constant term. Let F0 be its zero-constant primitive. Find F0(3)+(1), retaining the actual additive constant. Give a reduced fraction with positive denominator, retaining /1 for integers.

Definition and scope

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.

• mko-antiderivative

Step-by-step derivation

domain=R; coefficient lists are in ascending powers

constant term first; rational pairs=[numerator,denominator]

f coefficients ascending=[0]

seek F₀ with constant coefficient0 and F₀′=f

primitive coefficient at degree1 := div(0, 1)

primitive coefficient at degree1 = 0

differentiate back coefficient0 := mul(0, 1)

differentiate back coefficient0 = 0

[0]

all derivative coefficients agree with f

constant coefficient+C := sum(0, 1)

constant coefficient+C = 1

F(x) multiply at degree0 := mul(0, 3)

F(x) multiply at degree0 = 0

F(x) add coefficient0 := sum(0, 1)

F(x) add coefficient0 = 1

x=3; additive constant=1

F(x)=1/1

Reverse checks

• S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S008 · premise_and_result_audit — Recompute F(x) add coefficient0 with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute F(x) multiply at degree0 with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute constant coefficient+C with exact rational arithmetic, not rounded decimals.
• 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 differentiate back coefficient0 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute primitive coefficient at degree1 with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

1/1

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.