# Take-home Quiz

```MVC
Quiz #8
NAME:
Instructions: SHOW ALL WORK !! Exam is due at beginning of class on Thursday 9/12. Consult
no other person regarding these questions. You may not use the internet. (You may use other
references including your notes, calculator, Mathematica, and text.) Read the following paragraph
and sign it.
I have neither given nor received assistance on any of these questions. I understand that the penalty
for cheating on this exam is a D in the course.
Date
Signature
dy dx
, where D is the
2 2
x
y

1
D
region bounded by the graphs of xy  1, xy  4, y  1, and y  2. You might find it useful to sketch
the region D.
#1 Use a change of variables to simplify your task of evaluating 
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#2. Convert
 ( x  y)dxdydz
to an equivalent integral in spherical coordinates, where D is the
D
region below the sphere x 2  y 2  z 2  1 and above the cone z  3x 2  3 y 2 . You need not
evaluate the integral.
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#3 Find the volume of the
x 2  y 2  1, x 2  z 2  1, and y 2  z 2  1
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intersection
of
the
three
solid
cylinders
```