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A triple integral operator used to integrate functions over three-dimensional regions in multivariable calculus.

\iiint image

Examples

Triple integral over a volume

VdV=Vdxdydz\iiint_V dV = \iiint_V dx\,dy\,dz
\iiint_V dV = \iiint_V dx\,dy\,dz

Triple integral with specific bounds

[0,1]3xyzdxdydz\iiint_{[0,1]^3} xyz\,dx\,dy\,dz
\iiint_{[0,1]^3} xyz\,dx\,dy\,dz

Triple integral in spherical coordinates

Vr2sinϕdrdϕdθ\iiint_V r^2\sin\phi\,dr\,d\phi\,d\theta
\iiint_V r^2\sin\phi\,dr\,d\phi\,d\theta