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Percentage Calculator
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Integral Calculator
Calculate definite integrals numerically: enter f(x) and the limits to get the area under the curve with Simpson’s rule and an error check.
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How to use this calculator
Enter your values. The result updates as you type; press Calculate to confirm and jump to the result on mobile. Use Share to send the calculator with your result.
What this calculates
The definite integral ∫ₐᵇ f(x) dx is the signed area between the curve and the x-axis from a to b. It’s computed with Simpson’s rule, which fits parabolas to small slices of the curve and is very accurate for smooth functions.
∫ₐᵇ f(x) dx ≈ h/3 · [f(x₀) + 4f(x₁) + 2f(x₂) + … + 4f(xₙ₋₁) + f(xₙ)], h = (b − a)/n
Example
∫₀² (x² + 3x) dx: the antiderivative is x³/3 + 3x²/2, so the exact value is 8/3 + 6 = 8.6667, matching the calculator.
Limits
- No indefinite integrals (antiderivative + C).
- Improper integrals with an asymptote inside the interval are not supported.
- Trig functions use radians.
Frequently asked questions
What is the integral of x² from 0 to 3?
9 (x³/3 evaluated from 0 to 3).
Can it do indefinite integrals?
No, it evaluates definite integrals numerically.
About this tool
- Written by
- [Author: to be assigned]
- Reviewed by
- Formula tests passed · human review pending
- Last updated
- 31 Oct 2026
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