Question

Identify the quantities determined by the integral expressions.

$\rho (x,y)$ is density function.

${\iint }_{\Omega }xdA\text{and}{\iint }_{\Omega }ydA$

Short answer

The quanitities determined are moments.

Step-by-step solution

Given Information

It is given that expressions are

${\iint }_{\Omega }xdA\text{and}{\iint }_{\Omega }ydA$

$x,y$measured in centimeters.

Identification of the quantities

${\iint }_{\Omega }xdA$represents first moment about $y$axis having constant density function $\rho (x,y)=1$

${\iint }_{\Omega }ydA$represents first moment about $x$axis having constant density function $\rho (x,y)=1$

Moment will me measured in grams/cm.

Hence, moment about $y$axis is $M_y={\iint }_{\Omega }xdA$

Moment about$x$axis is$M_x={\iint }_{\Omega }ydA$