Ayaan Barr

2022-07-09

Please explain the antiderivative
Can someone please explain what an antiderivative is. Is there a rule for finding the general antiderivative of a function?

Tatiana Gentry

Expert

Explanation:
An antiderivative of a function f, with domain D, is a function F, with domain D, such that $\frac{d}{dx}F\left(x\right)=f\left(x\right)$ for all $x\in D$. If F and G are antiderivatives for f, then $F\left(x\right)=G\left(x\right)+C$ for all $x\in D$ and for some constant C. One can find the family of antiderivatives (which contains all antiderivatives, where they only differ by a constant) by computing the indefinite integral of f:
provided f is integrable of course.

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