9.8.10 Surface integrals

30 Problem: Calculate the surface integral of the \( 1^{\text {st }} \) kind: \[ \iint_{\sigma}(3-2 z) d \sigma, \] where \( \sigma:\left\{\begin{array}{c}z=1-\frac{y^{2}}{2} \\ y=x, x=0, \quad z=0\end{array}\right. \)