Online calculus solver

This calculus solver computes two of the most common calculus tasks numerically: the derivative of a function at a chosen point, and the definite integral of a function between two limits. Enter your function f(x), choose the derivative or integral tab, fill in the values, and get an accurate result instantly — useful for checking homework and understanding how a function behaves.

Derivatives and integrals explained

The derivative f '(x) measures the instantaneous rate of change of a function — the slope of the tangent line at a point. The definite integral measures the signed area under the curve between two x-values. This tool finds the derivative using a central-difference approximation and the integral using Simpson's rule with 2,000 intervals, which gives results accurate to several decimal places for smooth functions.

Function syntax

Write functions using +, −, *, /, and ^ for powers, with sin, cos, tan, sqrt, exp, ln, and log (base 10) available, plus pi and e. For example, x^3 - 2*x, sin(x), or exp(-x^2). To plot a function visually, use our graph plotter; for step-by-step area approximation, see the Simpson's rule calculator.

Frequently asked questions

Is the answer exact?

It is a high-accuracy numerical estimate, not a symbolic formula. For smooth functions it typically matches the exact value to 6–8 significant figures.

Can it integrate any function?

It works for continuous functions over the interval. Functions with a vertical asymptote between the limits (such as 1/x across zero) may give unreliable results.