Find the centroid of the region D, lying above the sphere x2+y2+z2 and below the paraboloid z=4-x2-y2.
The Attempt at a Solution
I decided it might be easier to change it to polar coordinates soo I did
where z goes from sqrt(6-r2) to 4-r2
θ goes from 0 to 2∏
then i thought the r would be where the two functions intersect, so i set sqrt(6-r2)=4-r2 solving for r i got my solutions came out to be sqrt2 and sqrt5, i dont know which one to use because i thought r would go from 0 to either sqrt2 or sqrt5
if some one could help me out i would really appreciate it.. thanks
solving for r i got