- #1

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## Homework Statement

Find the centroid of the region D, lying above the sphere x

^{2}+y

^{2}+z

^{2}and below the paraboloid z=4-x

^{2}-y

^{2}.

## Homework Equations

## The Attempt at a Solution

I decided it might be easier to change it to polar coordinates soo I did

M=∫∫∫ dzrdrdθ

where z goes from sqrt(6-r

^{2}) to 4-r

^{2}

θ goes from 0 to 2∏

then i thought the r would be where the two functions intersect, so i set sqrt(6-r

^{2})=4-r

^{2}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