Integral Calculator (symbolic + numeric)

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

Tranche

tranche-8

Evidence ID

t8-021

Ledger rows

1

No ledger note is attached.

Review findings

The stated Simpson method and the symbolic antiderivative examples are mathematically correct under the documented assumptions, but the specification needs review because Simpson constraints, error estimation, signed-versus-unsigned output, and the scope of the claimed always-available numeric fallback are not fully defined.

Formula and scope findings

• Simpson's rule is correct only with equally spaced samples, n subintervals, h=(b-a)/n, and an even positive integer n; these constraints are not stated.
• The required numeric error-estimation method is unspecified. A single Simpson evaluation does not itself provide an error estimate; Richardson comparison or another documented method is needed.
• The claim that numeric fallback is always available is too broad unless the implementation specifies handling for singularities, discontinuities, divergent integrals, overflow, and non-finite function values.
• The output says numeric area, but a definite integral is generally a signed quantity; the instrument must distinguish signed integral from geometric area.
• The symbolic method is described as nerdamer/math.js rules rather than a defined algorithm, so branch conventions, constants of integration, special functions, and unsupported forms are ambiguous.

Unit assumptions

• Bounds must use the same unit, and the integrand's output unit is function-unit multiplied by bound-unit.
• Polynomial and exponential test functions treat x as dimensionless unless a scale constant is explicitly supplied.
• Trigonometric functions use radians; the zero-boundary vector therefore uses radians.
• Definite integrals below are signed integrals, not absolute geometric areas.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The input 1/x over [-1,1] forces the quadrature to evaluate 1/0 and the ordinary definite integral is undefined. A calculator that returns a finite number, such as the Cauchy principal value 0, without explicitly identifying the principal-value convention would be incorrect.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "function": "3*x^2 - 4*x + 1",
    "variable": "x",
    "bounds": null
  },
  "expected_outputs": {
    "antiderivative": "x^3 - 2*x^2 + x + C",
    "spot_checks": [
      {
        "at": 1,
        "input_side": 0,
        "answer_side": 0
      },
      {
        "at": 2,
        "input_side": 5,
        "answer_side": 5
      }
    ]
  },
  "reference_data": {
    "method": "Differentiate the proposed antiderivative and compare with the integrand."
  },
  "working": "Let F(x)=x^3-2*x^2+x. Then F'(x)=3*x^2-4*x+1. At x=1: original=3(1)^2-4(1)+1=0; answer-side derivative=3(1)^2-4(1)+1=0. At x=2: original=3(2)^2-4(2)+1=12-8+1=5; answer-side derivative=12-8+1=5."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche8/tranche8-results.json
• BOUNDARY_HAZARD_CATALOG.json