Frequently Asked Questions

A definite integral ∫ₐᵇ f(x)dx represents the signed area between a function's curve and the x-axis, between the bounds a and b.

Simpson's rule is a numerical integration method that approximates a definite integral by fitting parabolas through groups of points, giving very accurate results even with a moderate number of subintervals.

For polynomial functions (sums of terms like c·xⁿ) and functions of the form 1/x, the calculator derives the antiderivative using the power rule and the natural log rule. For other functions, only the numeric result is shown.

The calculator uses Simpson's rule with 2000 subintervals, which is accurate to many decimal places for smooth, continuous functions over the chosen interval.

Any function math.js can parse, including polynomials, trigonometric functions, exponentials, logarithms, and rational functions like 1/x.

Yes. If a is greater than b, the calculator computes the integral over [b, a] and applies the sign flip, matching ∫ₐᵇ f(x)dx = −∫ᵦᵃ f(x)dx.

If the function produces a non-finite value anywhere in the interval (such as 1/x at x=0), the calculator flags that the integral cannot be computed over that range.

It states that if F is an antiderivative of f, then the definite integral of f from a to b equals F(b) − F(a). The calculator uses this to verify the numeric result when a symbolic antiderivative is available.

Yes, enter your function and bounds to instantly verify a definite integral, and compare against the symbolic antiderivative when available.

Yes, the integral calculator is completely free with no sign-up, and all calculations run instantly in your browser.