(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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}.

2. Relevant equations

3. 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

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# Homework Help: Centroid in three dimensions

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