f(x) =
sin cos tan exp log sqrt abs ln PI E pi
a lower
∫
b upper
The definite integral ∫ₐᵇ f(x) dx is the signed area between f(x) and the x-axis on [a, b].
For ±∞ limits, Nabla uses Double Exponential (Tanh-Sinh) quadrature — the gold standard for improper and singular integrals.
Trapezoidal / Simpson — classical Newton-Cotes. Predictable, use large N.
Gauss-Legendre 32pt — exact for polynomials ≤ deg 63.
Adaptive G7K15 — error-controlled, auto-refines near oscillations.
Double Exponential — Tanh-Sinh / Exp-Sinh transform. Best for singularities, ±∞, Γ, sinc, oscillatory integrands.
Monte Carlo — stochastic, converges as 1/√N.
Method
Newton-Cotes
High-order / Adaptive
Improper / Special
Composite Trapezoidal Rule — linear polynomial approximation per sub-interval.
Output
Enter a function, set limits, and compute.