\iiint

The \iiint command in LaTeX is used to represent a triple integral, which is an integral of a function in three variables over a three-dimensional region. It is commonly used in multivariable calculus to compute volumes, masses, and other quantities that depend on three variables.

Examples

Triple integral of a function f over a volume V.

\iiint_V f(x, y, z) \, dx \, dy \, dz

Triple integral over a cubic region to find the sum of squares of coordinates.

\iiint_{\text{cube}} (x^2 + y^2 + z^2) \, dx \, dy \, dz

Triple integral in spherical coordinates over a spherical region.

\iiint_{\text{sphere}} \rho^2 \sin\phi \, d\rho \, d\phi \, d\theta