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%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Tue Oct 26 16:16:53 2004}
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Ma227\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad
\qquad Test \ 1\qquad \qquad \qquad\ October 6, 2003

\vspace{1pt}

Name:

Pledge:

\vspace{1pt}

SHOW ALL WORK. \ \ NO CALCULATORS OR\ PCs ALLOWED.

\vspace{1pt}

I.) \ (15)\qquad Reverse the order of integration. \ \textbf{(DO\ NOT\
INTEGRATE)}

\vspace{1pt}

\qquad \qquad \qquad \qquad $\dint_{-1}^{2}\dint_{y^{2}-3}^{y-1}\left(
x^{2}+xy\right) dxdy$

\vspace{1pt}

\pagebreak

\vspace{1pt}

II.) \ (15)\qquad Find the surface area that is cut from \ $z=xy$ \ by \ $%
x^{2}+y^{2}=1$.

\vspace{1pt}

\pagebreak

\vspace{1pt}

III.) \ (20)\qquad Find the mass and the centroid of the lamina which is
bounded

\qquad \qquad \qquad\ by \ $x^{2}+y^{2}\leq a^{2};$ \ $y\geq 0;$ \ if the
density at any point is proportional

\qquad \qquad \qquad\ to its distance from the origin.

\vspace{1pt}

\pagebreak

\vspace{1pt}

IV.) \ (15)\qquad Set up a triple integral in \textbf{spherical coordinates }%
to find the volume

\qquad \qquad \qquad\ \ of the solid bounded below by \ $z^{2}=3x^{2}+3y^{2}$
\ and bounded above

\qquad \qquad \qquad\ \ by \ $x^{2}+y^{2}+z^{2}=2z.$ \ \ \textbf{(DO NOT\
INTEGRATE.)}

\vspace{1pt}

\pagebreak

\vspace{1pt}

V.) \ (15)\qquad Rewrite the following double integral in polar coordinates.

\qquad \qquad \qquad\ \textbf{(DO\ NOT\ INTEGRATE.)}

\vspace{1pt}

\qquad \qquad \qquad \qquad \qquad $\dint_{0}^{2}%
\dint_{2x}^{4}x^{2}y^{2}dydx $

\vspace{1pt}

\pagebreak

\vspace{1pt}

VI.) \ (20)\qquad Set up a triple integral in \textbf{Cartesian coordinates }%
to find the

\qquad \qquad \qquad\ \ volume of the solid bounded by \ $z=2x^{2}+2y^{2}$ \
and

\qquad \qquad \qquad\ \ $z=48-x^{2}-y^{2}.$ \ \ \textbf{(DO\ NOT\ INTEGRATE.)%
}

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