Category:Triple Integrals

This category contains results about Triple Integrals.
Definitions specific to this category can be found in Definitions/Triple Integrals.

Let $f: \R^3 \to \R$ be a real-valued function of $3$ independent variables.

The triple integral of $f$ with respect to those independent variables is defined as:

$\ds \map \int {\iint \map f {x, y, z} \rd x \rd y} \rd z$

where:

$\map f {x, y, z}$ is integrable

$\ds \iint \map f {x, y, z} \rd x \rd y$ is the double integral with respect to $\paren {x, y}$ of $\map f {x, y, z}$, keeping $z$ constant

and is denoted:

$\ds \iiint \map f {x, y, z} \rd x \rd y \rd z$