[See Solution] Use spherical polar coordinates to calculate the exact value of the triple integral ∫_R(x^2+y^2) d x d y d z where R is the hemispherical
Question: Use spherical polar coordinates to calculate the exact value of the triple integral
\[\iiint_{R}\left(x^{2}+y^{2}\right) d x d y d z\]where \(R\) is the hemispherical region that lies above the plane \(z=0\) but below the sphere \(x^{2}+y^{2}+z^{2}=1\)
Deliverable: Word Document 
![[Solution] Use the change of variables x=1/2(u+v),](/images/solutions/MC-solution-library-46817.jpg "[Solution] Use the change of variables x=1/2(u+v), y=1/2(u-v)")
[Solution] Use the change of variables x=1/2(u+v), y=1/2(u-v)
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