I.11.12 Triple integrals

Calculate the surface integral using the Gauss-Ostrogradsky formula: \[ \iint_{S} y d x d z, \text { where } S: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=1 . \]