∫Integral Calculator

Compute a definite integral with Simpson's rule, and see the symbolic antiderivative for polynomial and 1/x functions.

Function f(x)

Lower bound a

Upper bound b

Calculations run entirely in your browser using math.js for parsing and evaluation, with Simpson's rule for the definite integral. No data is sent to a server.

Free Integral Calculator

Our free integral calculator computes the definite integral of a function over an interval [a, b] using Simpson's rule, a numerical method accurate to a very high number of decimal places for smooth functions. Enter any function — polynomial, trigonometric, exponential, or rational — along with the bounds, and get an instant result.

For polynomial functions and functions of the form 1/x, the calculator also derives the symbolic antiderivative using the power rule (∫xⁿ dx = xⁿ⁺¹/(n+1)) and the natural log rule (∫1/x dx = ln|x|), then evaluates it at both bounds using the Fundamental Theorem of Calculus to confirm the numeric result.

This makes the tool useful for checking calculus homework, verifying area-under-the-curve calculations, and understanding how a definite integral connects to its antiderivative. No sign-up, no downloads — everything runs instantly in your browser.