Schey 003: Surface Integral over Half Sphere

test

$\left[ \begin {array}{ccc} \sin \left( \phi \right) \cos \left(
\theta \right) &-R\sin \left( \phi \right) \sin \left( \theta \right)
&R\cos \left( \phi \right) \cos \left( \theta \right)
\\ \noalign{\medskip}\sin \left( \phi \right) \sin \left( \theta
\right) &R\sin \left( \phi \right) \cos \left( \theta \right) &R\cos
\left( \phi \right) \sin \left( \theta \right) \\ \noalign{\medskip}
\cos \left( \phi \right) &0&-R\sin \left( \phi \right) \end {array}
\right]$