Dedicated to Comrade Otto Bretscher.

Calculus Level 5

Let \(S\) be the surface: \[z=x(1-x)y(1-y)\]

Such that

\(0\leq x,y\leq 1\)

Evaluate the integral:

\[\int \int_{S} x\mathbf{k}.d\mathbf{A}\] where \(d\mathbf{A}\) is the upward-pointing normal vector.

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