Definition:Primitive (Calculus)/Indefinite Integral
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Definition
Suppose that the real or complex function $F$ is a primitive of the function $f$.
From the Fundamental Theorem of Calculus, it is apparent that to find the value of a definite integral for a function between two points, one can find the value of the primitive of the function at those points and subtract one from the other.
Thus arises the notation:
- $\displaystyle \int f \left({x}\right) \ \mathrm d x = F \left({x}\right) + C$
where $C$ is the arbitrary constant.
In this context, the expression $\displaystyle \int f \left({x}\right) \ \mathrm d x$ is known as the indefinite integral of $f$.
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: $\S 14$
