Numerical Integration Calculator
Evaluate definite integrals ∫ab f(x) dx with adaptive Simpson's rule (absolute tolerance 1e-10). Type any expression in x.
Integral
Use ^ for powers, e.g. x^2*sin(x). Functions: sin cos tan asin acos atan exp log ln sqrt abs. Constants: pi, e.
How it works
Adaptive Simpson's rule recursively subdivides the interval where the integrand is hardest to approximate, until the estimated error drops below 1e-10. Smooth functions converge in milliseconds; sharp peaks and oscillations automatically get finer subdivisions where they need them. Your expression is parsed by a small recursive-descent parser — never eval() — so it is safe to type anything.
Frequently asked questions
What expression syntax is supported?
Operators + − * / ^ and parentheses; functions sin cos tan asin acos atan exp log ln sqrt abs; constants pi and e; the variable x. Examples: x^2*sin(x), 1/(1+x^2), exp(-x^2).
How accurate are the results?
The integrator targets an absolute error below 1e-10. For smooth integrands the result is typically accurate to 10+ digits. The method and compute time are reported with every result.
What about singularities or infinite limits?
Improper integrals are not handled directly — split the interval at the singularity, or substitute first (e.g. a tangent substitution for infinite limits). Highly oscillatory integrands may need a nudge: split the interval at the zeros.
Is my data sent to a server?
No. Every computation runs in JavaScript in your own browser. Nothing you type ever leaves your device.