Triple Integral

A Multiple Integral with 3 variables over ${\mathbb{R}}^3$.

Triple Integral as Riemann Sum

For bounded function $f:{\mathbb{R}}^3\to \mathbb{R}$, we define:

$$\int \int {\int }_{R}fdV=\underset{n\to \infty }{\lim }\sum _{i,j,k=0}^{n-1}f(c_{ijk})△x△y△z$$