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\textbf{Math 225: Calculus III}
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\textbf{Quiz 10}\quad \textsl{December 4, 2003}
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\bigskip

1. Compute the surface integral $\iint_S(1-z)\,dS$ where $S$ is the unit
upper hemisphere, $z = \sqrt{1-x^2-y^2}$.

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2. Let $S$ be the surface parameterized by $\r(u,v) = \langle u\cos(v),
v/\pi, u\sin(v)\rangle$, $0 \le u \le 1$, $0 \le v \le 4\pi$. Compute
the flux integral $\iint_S \F\cdot\n\,dS$ where $\F(x,y,z) = x\i + y\j +
z\k$ and $\n$ is the unit normal to $S$ oriented in the positive $y$
direction.
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