Let (S) be the part of the graph (z=g(x, y)) lying over a domain (mathcal{D}) in the

Question:

Let $S$ be the part of the graph $z=g(x, y)$ lying over a domain $\mathcal{D}$ in the $x y$-plane. Let $\phi=\phi(x, y)$ be the angle between the normal to $S$ and the vertical. Prove the formula

\[
\operatorname{area}(S)=\iint_{\mathcal{D}} \frac{d A}{|\cos \phi|}
\]

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