Category:Primitives

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This category contains results about Primitives in the context of Calculus.
Definitions specific to this category can be found in Definitions/Primitives.


Primitive of Real Function

Let $F$ be a real function which is continuous on the closed interval $\left[{a \,.\,.\, b}\right]$ and differentiable on the open interval $\left({a \,.\,.\, b}\right)$.

Let $f$ be a real function which is continuous on the open interval $\left({a \,.\,.\, b}\right)$.


Let:

$\forall x \in \left({a \,.\,.\, b}\right): F' \left({x}\right) = f \left({x}\right)$

where $F'$ denotes the derivative of $F$ with respect to $x$.


Then $F$ is a primitive of $f$, and is denoted:

$\displaystyle F = \int f \left({x}\right) \, \mathrm d x$

Subcategories

This category has the following 54 subcategories, out of 54 total.

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Pages in category "Primitives"

The following 43 pages are in this category, out of 43 total.

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