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Formula verified · Deterministic calculation

Integral Calculator

Enter a supported function and finite lower and upper bounds. CalcuMint uses independently refined composite Simpson estimates and reports numerical error information.

Definite integral9
Estimated error
0.00021255324
Refinement intervals
16,384

Trend

2.255.06
2.45.76
2.556.5
2.77.29
2.858.12
39
Methodology

The same restricted deterministic expression engine feeds independently refined composite Simpson estimates with explicit convergence checks.

Sources
  • CalcuMint deterministic numerical-calculus engine
Solution steps
  1. Parse f(x) = x^2
  2. Integrate from 0 to 3 with adaptive Simpson refinement
  3. Integral ≈ 9; estimated error ≈ 0.00021255323646762747; intervals = 16384

How this calculator works

Composite Simpson estimates are repeatedly refined; convergence is accepted only after independent refinements agree within the configured tolerance.

Formula

∫ₐᵇ f(x)dx via independently refined composite Simpson estimates

Computes a finite definite integral and reports an estimated numerical error.

Worked example

Integral of x² from 0 to 3 is a verified test case used by the calculation engine.

Assumptions and limitations

  • This calculator evaluates finite definite integrals numerically.
  • The expression must remain finite at all sampled points in the interval.
  • Highly difficult or improper integrals may be rejected rather than returning an unreliable value.

Methodology & sources

This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.

  • CalcuMint deterministic numerical-calculus engine — Adaptive composite Simpson refinement with convergence checks.

Frequently asked questions

Does it find an antiderivative?

No. It numerically evaluates the definite integral over the bounds you provide.

Why can an integral be rejected?

The engine rejects calculations that do not demonstrate convergence within its supported refinement budget.

Related calculators

Derivative CalculatorEstimate a function derivative at a point with deterministic numerical refinement.Limit CalculatorEstimate finite one-sided or two-sided limits with convergence checks.