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\textbf{Math 225: Calculus III}
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\textbf{Quiz 7}\quad \textsl{Mar. 25/27, 1997}
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\begin{enumerate}
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\item 
Calculate the integral of $f(x,y) = \sin[\pi(x^2+y^2)]$ over the unit disk,
$x^2 + y^2 \le 1 $.

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\problemspace
\item 
Find the average height of points in the bottom corner of a unit cube. The
corner is defined to be the solid region below the plane $x + y + z = 1$ in
the first octant. Its volume is $1/6$. The height function is, of course,
$f(x,y,z) = z$.
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