Q. 19 - Calculus

Question

Identify the quantities determined by the integral expressions in Exercises $19–24$. If $x, y,$ and $z$ are all measured in centimeters and $\rho (x, y,z)$ is a density function in grams per cubic centimeter on the three-dimensional region $\Omega$, give the units of the expression.

$\underset{\Omega }{\iiint }dV$.

Step-by-Step Solution

Answer

The given triple integral $\underset{\Omega }{\iiint }dV$ represents the volume of the solid $\Omega$ and the units are cubic centimeter.

Step 1 . Given information

$\underset{\Omega }{\iiint }dV$.

Step 2 . Unit for the given triple integral:

By the definition of triple integral, the triple integral $\underset{\Omega }{\iiint }dV$ represent the volume of the solid region $\Omega$ and the units for the volume is cubic units.

Hence by using this definition, the given triple integral represents the volume of the solid $\Omega$ and the units are cubic centimeter.