Is this a symbolic or numerical result?

Numerical: it does not return a derivative formula but the value at the point you choose and the integral over the interval you choose — accurate enough for homework and engineering estimates.

How accurate is the derivative?

Central differences with Richardson extrapolation typically give an error around 1e-10 for smooth functions; results are shown to 10 significant digits.

What if the interval contains a discontinuity?

The tool warns that the integrand is infinite or discontinuous. Split the interval at the problem point and integrate each piece separately.

How do I write the function?

Exactly as in the graphing tool: ^ for powers, implicit multiplication (2x), functions sin cos tan ln lg sqrt abs exp and constants pi, e.

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∫Online Derivative and Definite Integral Calculator

Type a function and get derivatives and integrals. The derivative view gives f(x₀), the first and second derivatives, the tangent and normal lines and the slope angle; the integral view uses adaptive Simpson’s rule and reports an error estimate and the average value on the interval.

Free · No sign-up · Runs in your browserLast updated: 2026-10-26

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How to use Derivative & Integral

1Choose “Numerical derivative” or “Definite integral”
2Enter f(x), for example x^2*sin(x), 1/(1+x^2) or e^(-x^2)
3Enter the point x₀, or the limits a and b — results update as you type

FAQ

Is this a symbolic or numerical result?: Numerical: it does not return a derivative formula but the value at the point you choose and the integral over the interval you choose — accurate enough for homework and engineering estimates.
How accurate is the derivative?: Central differences with Richardson extrapolation typically give an error around 1e-10 for smooth functions; results are shown to 10 significant digits.
What if the interval contains a discontinuity?: The tool warns that the integrand is infinite or discontinuous. Split the interval at the problem point and integrate each piece separately.
How do I write the function?: Exactly as in the graphing tool: ^ for powers, implicit multiplication (2x), functions sin cos tan ln lg sqrt abs exp and constants pi, e.