MathProblemsBank

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.