Finding the z-coordinate of the center of gravity for a region

[rman144]

(Moderator's note: thread moved from Calculus and Analysis)

I just need to know if my answer is correct for the following:

Find the z-coordinate of the center of gravity of the region:

(x/(z^3-1))^2 + (y/(z^3+1))^2<=1, 0<=z<=1.

I'm getting 7/16; am I in the ballpark? Thanks for any help.

 

[arildno]

I got that value as well.

 

[rman144]

Thanks; glad to know I'm at least somewhat following this material.