About this tool
The Definite Integral Calculator is a free, in-browser calculus tool that computes the signed area under a curve — the definite integral of f(x) from a lower limit a to an upper limit b. It uses composite Simpson's rule, a high-accuracy numerical method that fits parabolas across pairs of subintervals: with h = (b − a)/n it evaluates (h/3)·[f(x₀) + f(xₙ) + 4·Σf(odd) + 2·Σf(even)]. The number of subdivisions n (default 1000, kept even) is adjustable for more precision.
All computation happens locally in your browser, so nothing you enter is transmitted anywhere. You can type the integrand with +, −, *, / and ^, parentheses, the constants pi and e, and functions like sin, cos, exp, ln and sqrt. The bounds accept plain numbers or small expressions such as pi or 2*e, and you may enter inf or -inf for improper integrals, which the tool handles by truncating at a large finite limit and noting the approximation.
When the integrand is a polynomial (a sum of terms like c·xᵏ), the calculator also derives an exact symbolic antiderivative F(x) and cross-checks the numerical answer against F(b) − F(a) via the Fundamental Theorem of Calculus. For example, the integral of x² from 0 to 1 is exactly 1/3 ≈ 0.3333333, matching both the Simpson estimate and the antiderivative x³/3.