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\textbf{Math 225: Calculus III}
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\textbf{Quiz 8}\quad \textsl{April\ 4/6, 1995}
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\item 
Let $D$ be the solid hemisphere $0 \le x^2 + y^2 + z^2 \le 4$, $z \ge
0$. Compute the integral of $\sqrt{x^2 + y^2 + z^2}$ over $D$.
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\problemspace
\item 
Let $R$ be the region defined by $-3 \le x + 5y \le 3$, $0 \le 2x + 7y
\le 4$.  Use the change of coordinates $u = x + 5y$, $v = 2x + 7y$ to
transform the integral $\iint_R x y^2\,dA$ into an iterated integral in
the $uv$-plane. (Do not evaluate the integral.)

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