Antiderivative
Find F such that F′(x) = f(x). The general solution is F(x) + C. Power rule: ∫ xn dx = xn+1/(n+1) + C for n ≠ −1. ∫ 1/x dx = ln|x| + C.
Definite integral
If F is an antiderivative of f on [a, b], then ∫ab f(x) dx = F(b) − F(a). Geometry: signed area between the graph and the x-axis.
When there is no elementary F
The calculator falls back to Simpson’s rule on a fine mesh if both bounds are finite numbers. That is an estimate, not an exact fraction.
FAQ
Multiple integrals?
This page is one variable. Nested integrals are not parsed as area/volume commands.
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