Problem

(Q) Let $S$ be the surface described by $z=x^2+\dfrac{y^2}{2}$ with $4x^2+y^2\le 1$ oriented with normals with positive $k$-components. Let $\mathbf{F}(x,y,z)=x\mathbf{i}-y\mathbf{j}+\mathbf{k}$. Evaluate $\iint_S \mathbf{F}\cdot \mathrm{d}\mathbf{S}$. Answer: $\underline{\quad(18)\quad}$. Also, evaluate $\iint_S \mathrm{d}S$. Answer: $\underline{\quad(19)\quad}$.