Definite Integral Calculator
Apply the power rule for integration and evaluate the Fundamental Theorem of Calculus step by step.
Verify this calculatorMaintained
See what the result uses—and what it cannot know.
Sumvoro calculates deterministically from the visible inputs. It does not invent lender terms, local rules, market values, medical facts, or professional judgments.
- 1 · InputsCheck every entered value against the latest statement, quote, measurement, or official source.
- 2 · Formula
An antiderivative of ax³ + bx² + cx + d is ax⁴/4 + bx³/3 + cx²/2 + dx. The definite integral is F(upper) − F(lower). - 3 · SensitivityUse Insights to run a lower and higher case. If the conclusion changes easily, collect better information or leave more margin.
- 4 · ScopeThis tool is maintained and covered by automated calculation tests. Provider timing, rounding, and omitted facts can still change a real-world result.
- Formula release
- 2026.10-r4
- Release date
- October 10, 2026
- Review status
- Maintained
- Source review
- September 12, 2026
Optional readingLearn how this calculator works
How the definite integral calculator works
Integrate a cubic polynomial exactly between two bounds and show the antiderivative and signed area.
An antiderivative of ax³ + bx² + cx + d is ax⁴/4 + bx³/3 + cx²/2 + dx. The definite integral is F(upper) − F(lower).
Read our calculation methodology and limitations.
Example
The integral of x² from 0 to 3 is [x³/3]₀³ = 9.
What affects the result
- A definite integral is signed area; regions below the x-axis subtract.
- Reversing the bounds changes the sign.
- This tool integrates polynomials through degree three exactly.
Frequently asked questions
Is the result always geometric area?
It is signed area. Total geometric area requires splitting at every x-intercept and adding absolute areas.
Does this solve indefinite integrals?
It displays the antiderivative, but the primary result evaluates it between your entered bounds.