
9.8.2 Surface integrals
3
Problem:
Calculate using the Ostrogradsky formula:
\[
\int_{S} \int^{(x \cos \alpha+y \cos \beta+z \cos \gamma)} \underset{\sqrt{x^{2}+y^{2}+z^{2}}}{d s}
\]
where \( S=\left\{x^{2}+y^{2}+z^{2}=z\right\} \),
\( \vec{n}=(\cos \alpha, \cos \beta, \cos \gamma) \) is the outside normal.