91影视

Given expressions are:

${鈭�}_{惟}x蚁(x,y)dA\text{and}{鈭�}_{惟}y蚁(x,y)dA$

The objective of this problem is to identify the quantity determined by the integral expression. x and y are measured in centimeters and$蚁(x,y)$

is measured in grams per square centimeter. Give the units of expression.

The expressions are:

${鈭�}_{惟}x蚁(x,y)dA\text{and}{鈭�}_{惟}y蚁(x,y)dA$

The expression role="math" localid="1650533845071" ${鈭�}_{惟}x蚁(x,y)dA$represents the first moment about y - axis with uniform density. The expression role="math" localid="1650533837942" ${鈭�}_{惟}y蚁(x,y)dA$represents the first moment about x - axis with uniform density. If x and y are measured in centimeters and $蚁(x,y)$is measured in grams per square centimeter. Then, first moment will be measured in grams per centimeter.

Moments are symbolized according to the axis about which the moment is taken.

First moment about y - axis:

$M_y={鈭�}_{惟}x蚁(x,y)dA$

First moment about x - axis:

$M_x={鈭�}_{惟}y蚁(x,y)dA$