Definite Integral Calculator
Evaluate a definite integral over bounds, show exact antiderivative results when available, Simpson numerical approximation, method comparison, and signed area.
Definite integral with bounds
The English definite-integral intent is different from an antiderivative lookup: users need a number for a lower bound and an upper bound, often with a signed-area interpretation and numerical fallback.
When an antiderivative F is available, the Fundamental Theorem of Calculus turns the integral into a difference of endpoint values.
- Enter f(x), lower bound, and upper bound.
- Use pi, e, inf, or -inf when needed.
- Read whether the result is exact or a Simpson numerical approximation.
Numerical and signed-area outputs
| Output | Meaning |
|---|---|
| Exact | Antiderivative was found and evaluated at the bounds |
| Simpson approximation | Numerical fallback for harder functions |
| Method comparison | Left rectangles, right rectangles, trapezoids, and Simpson |
| Signed area | Area above the x-axis is positive; area below it is negative |
Frequently Asked Questions
Sources and References
- Definite Integral CalculatorSymbolab
- Integral CalculatorWolfram|Alpha
- Definite IntegralWolfram MathWorld
- Simpson's RuleWolfram MathWorld
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Find an antiderivative for supported elementary functions, include + C, verify by differentiation, and see the function and antiderivative chart.
Differentiate functions symbolically, choose first through third derivative, evaluate at a point, compare with a central-difference check, and view the tangent slope.
Estimate limits numerically for x approaching a point or infinity. Supports two-sided, left-hand, and right-hand checks with a convergence table and chart.
Plot formula. Add up to 5 functions, use common math functions, and compare curves on one graph.
Calculate ln(x), the natural logarithm with base e. Supports positive numbers, fractions, e powers, exact matches, and explanatory steps.