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\textbf{Math 225: Calculus III}
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\textbf{Quiz 9}\quad \textsl{Apr. 8/10, 1997}
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\begin{enumerate}
\problemspace
\item 
Let $R$ be the region in the first quadrant defined by
\[
\begin{array}{rcl}
1 \le & 2x^2 - y^2 & \le 2\\
1 \le & 2y^2 - x^2 & \le 2\\
\end{array}
\]
Use the change of variables $u = 2x^2 - y^2$, $v = 2y^2 - x^2$, to
transform the integral of $f(x,y) = x y$ into an iterated integral in $u$
and $v$.  (You do not need to evaluate the integral, but you should
simplify your answer.)
\[
\resizebox{1.5in}{!}{\includegraphics{quiz09.eps}}
\]
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\problemspace
\item 
Let $C$ be the curve $y = x^2$ from $0 \le x \le 1$. Evaluate the line
integral of $f(x,y) = \sqrt{y}$ over the curve~$C$.

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