# Definition:Primitive (Calculus)/Indefinite Integral

Jump to navigation
Jump to search

This page has been identified as a candidate for refactoring of medium complexity.In particular: Needs to be rewritten somewhat, as this page does not hang together as a definition page as it ought.Until this has been finished, please leave
`{{Refactor}}` in the code.
Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Refactor}}` from the code. |

It has been suggested that this page or section be merged into Definition:Primitive (Calculus).To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Mergeto}}` from the code. |

## 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:

- $\ds \int \map f x \rd x = \map F x + C$

where $C$ is the constant of integration.

In this context, the expression $\ds \int \map f x \rd x$ is known as the **indefinite integral** of $f$.

## Sources

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: Work out where this goes in the flowIf you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*: $\S 14$