Calculus Toolkit

Numerical calculus on a function f(x): compute definite integrals with Simpson's, trapezoidal, and midpoint rules; estimate the derivative at a point by a central difference; and find a root of f(x) = 0 by bisection (given a bracketing interval) or Newton's method. Expressions use + − * / ^, parentheses, the variable x, constants pi/e/tau, and common functions (sin, cos, exp, ln, sqrt, …) parsed by a safe recursive-descent parser — no eval. Everything runs locally in your browser.

f(x) =

Operators + − * / ^ (right-assoc, binds tighter than unary minus), parentheses, x, constants pi e tau, functions sin cos tan asin acos atan sinh cosh tanh exp ln log log2 sqrt cbrt abs floor ceil round sign.

Lower bound a

Upper bound b

Intervals n (even)

Simpson's rule approximates ∫ₐᵇ f(x)dx by fitting parabolas across pairs of intervals — exact for cubics, O(h⁴) error. The trapezoidal and midpoint rules give a sanity check (they converge to the same value as n grows). The derivative uses a central difference (f(x+h)−f(x−h))/(2h), O(h²). Bisection finds a root in [a, b] when f(a) and f(b) have opposite signs; Newton's method iterates x − f(x)/f′(x) from a guess (the derivative is computed numerically). Pairs with the Function Plotter and Statistics tools. Everything runs locally — nothing leaves your browser.