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\textbf{Math 225: Calculus III}
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\textbf{Quiz 10}\quad \textsl{April\ 25/27, 1995}
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\item 
Let $\CC$ be the cardiod $r = 3 + 2 \sin(\theta)$, $0 \le \theta \le 2\pi$, and let $\n$
be the outward unit normal vector to $\CC$. Use a version of Green's
Theorem to compute the flux integral $\int_\CC \F\cdot\n\,ds$ 
where $\F = -y\i + x\j$.

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\item 
Let $\Sigma$ be the portion of the paraboloid $z = 4 - x^2 - y^2$ in the first octant.
Compute the surface integral $\int_\Sigma z + x^2 + y^2\,d\sigma$.
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