Finding the Center of Mass of D

[yzc717]

Homework Statement

Let D be the region in the (x, y) plane bounded by the lines y=x, y=4x and the hyperboals xy=1 and xy=9. find the center of mass of D.

Homework Equations

The Attempt at a Solution

My thought: to use the center of mass formula? and use the change of variables?

 

[HallsofIvy]

What have you done? The problem is to find a center of mass- why should there be a "?" on "use the center of mass formula"? Of course you shold use it. I can't speak toward "use the change of variables" because you haven't said what the integral is!


(Strictly speaking, this is NOT a "center of mass" problem at all because you have not given any density function so there is no "mass" and no "center of mass". It is a purely geometric "centroid" problem but that can be done exactly like a "center of mass" problem assuming constant density.)

 

[yzc717]

What have you done? The problem is to find a center of mass- why should there be a "?" on "use the center of mass formula"? Of course you shold use it. I can't speak toward "use the change of variables" because you haven't said what the integral is!


(Strictly speaking, this is NOT a "center of mass" problem at all because you have not given any density function so there is no "mass" and no "center of mass". It is a purely geometric "centroid" problem but that can be done exactly like a "center of mass" problem assuming constant density.)

the problem is not given one.

do I have to find the area of the two regions first?

Then what do I do next?