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Math 20B
Final Exam (200 points)
3 PM
March 23, 2001
Section
Print Name
Signature
ID #
•
Use this exam for your work.
Do NOT use a blue book
.
•
Use the back of the exam pages if you need scratch paper.
•
The exam is CLOSED BOOK, but you may use ONE SHEET OF NOTES.
•
Calculators are NOT allowed.
•
You must show your work to receive credit.
1. (40 pts.) Let
R
be the region between the two parabolas
y
=
x
2
and
x
=
y
2
.
Let
V
be the volume obtained when
R
is rotated about the
y
axis.
(a) Sketch the region
R
. Include in your
drawing the coordinates of the point
where the parabolas intersect.
Set up (but
do not evaluate
) integrals for the following.
(b) The arc length of the boundary of
R
that is on the parabola
y
=
x
2
.
(c) The volume of
V
.
(d) The surface area of
V
.
Be careful
:
V
has what might be called an inner and outer surface.
The surface area is the sum of the areas of these two surfaces.
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This note was uploaded on 06/17/2009 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.
 Winter '08
 Justin
 Math, Calculus

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