Q 6. - Calculus

Question

Identify the quantities determined by the integral expressions

$\rho (x,y)$ y) is a density function in grams per square centimeter.

${\iint }_{\Omega }\rho (x,y)dA$

$\rho (x,y)$ is measured in grams per square centimeter.

Step-by-Step Solution

Answer

The expression represents mass of bounded region.

Step 1: Given Information

It is given that ${\iint }_{\Omega }\rho (x,y)dA$

$x,y$ is in centimeter

Step 2: Identification of the quantities

The expression ${\iint }_{\Omega }\rho (x,y)dA$ gives mass of bounded region.

As $x,y$ is calculated in centimeters and $\rho (x,y)$ in grams per square centimeter.

Hence, mass is in grams.

$m={\iint }_{\Omega }\rho (x,y)dA$