Triple Integral

It totals an integrand through a solid region. Its three strokes correspond to the coordinates x, y, and z. In ∭_E f(x,y,z)dV, E names the solid region and dV means a tiny piece of volume. If f=1, the result is E's volume; if f is density, it gives total mass.

∭ extends the single integral sign ∫; it was not invented as a special mark for three-dimensional work. Leibniz introduced ∫ in an unpublished manuscript in 1675, shaping it like a long s for summa, Latin for “sum.” The sign later appeared in print. Fourier's 1822 work is associated with the modern placement of definite-integral limits.

How do I type the triple integral symbol?

Use \iiint in LaTeX math mode. It produces a properly spaced triple integral, leaving room for limits and a differential such as dV.

For a standalone Unicode character in ordinary text, a Unicode-aware LaTeX input method can turn \iiint into ∭ after you press Space or Return.