math.numerical.definite_integral

Three distinct suites: educational examples on the calculator page, this legacy regression count (13/13 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.1.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-17.integral-input-surface-contract-v5. Calculation version 1.1.5. CVP 1.0.0-proposed. 177/177 golden · 2/2 CVP boundary · 13/13 invalid · 1/1 property · 3/3 metamorphic · 12/12 cross-interface · 1/1 cross-calculator · 6/6 CVP contract. digest 535933d707a3.

• Golden (oracle-backed) 177 / 177
• CVP boundary 2 / 2
• Invalid input 13 / 13
• Property 1 / 1
• Metamorphic 3 / 3
• Cross-interface 12 / 12
• Cross-calculator 1 / 1
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 2/2 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity.
• Verified scope all published methods
• Assurance Core

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:aec9270abf71e660b92391c8967133c9838a3024b92ee599376460284ceb300f

Input schema sha256:980ad6cc59e311f5f5a7bfc8a62a3507b8459ea47c77fb49e52b775d035bd7b1 · Output schema sha256:249d911579c3c854401380ab0b3ca96eaa1ea6f7a4ffb37c946ff076cb312a90 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

definite-integral

Engine

definite-integral

Engine build

2026-10-17

Evidence core

2026-10-17T06:05:53.872Z

Rendered

2026-10-23T01:27:11.650Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of the integrand on [a, b] (true f shaded; trapezoid/Simpson panel overlays when n≤16; Gauss nodes when method=gauss). Same fnValue as REST/MCP. Not indefinite CAS.
• Polynomial degree ≤ 8
• exact is a binary64 closed-form baseline, not symbolic exact arithmetic. abs_err retains the historical signed value: raw quadrature minus baseline; it is not an error bound.
• Reversed intervals change the sign; equal bounds return zero after input validation.
• Gauss n is nodes 2–8, not panels

Limitations

• Not indefinite / symbolic CAS integrate
• Simpson/trapezoid n panels 2–10000; Simpson n forced even
• Gauss–Legendre n nodes 2–8
• Polynomial degree ≤ 8
• Decimal nonzero-to-zero inputs and unresolved nonzero outputs are rejected (NUMERIC_UNDERFLOW).
• n must be an integer; odd Simpson n rounds up to the next even panel count.
• Integrand sample overflow/underflow and severe quadrature cancellation are rejected; rescale or split the interval.
• exact is a binary64 analytic baseline; abs_err is the signed raw quadrature-minus-baseline difference, not a certified bound.