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\vbox{\halign{\bf#\hss\cr Math 225: Calculus III\cr
Quiz 8\quad Mar. 29/31, 1994\cr
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1. Let $D$ be the portion of the solid sphere $x^2 + y^2 + z^2 \le 4$
{\sl below} the upper nappe of the cone $z^2 = x^2 + y^2$ and {\sl above}
the $xy$-plane. Use spherical coordinates to evaluate the integral
$\iiint_D(x^2 + y^2 + z^2)^{3/2}\,dV$ over $D$.


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2.  Let $R$ be the region defined by $(1/2)x \le y \le 2 x$, and $1 \le x y
\le 7$. Using the change of coordinates $u = x y$, and $v = y/x$, transform
the integral $\iint_R x y\,dA$ into an iterated integral in the
$uv$-plane.

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