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MATH 126
FINAL EXAM
December 15, 2004
Read the problems carefully and answer the questions asked. Write neatly and indicate
clearly your answer to each problem. The backs of the sheets may be used for scratch paper
or to continue your work on a problem. All problems count equally and you are to do all
ten problems. You must show your work to obtain full credit. Points may be deducted if
you do not justify your ﬁnal answer. Calculators, notes, books, or collaboration with others
are
not
allowed. If you have any questions about any of the problems ask the proctor, but
no one else!
1
. Let
R
be the region in the ﬁrst quadrant bounded by the curves
y
=
x
3
and
y
= 2
x

x
2
.
(i) Calculate the area of
R
.
(ii) Calculate the volume of the solid obtained by rotating
R
about the
y
axis.
2
. A circular swimming pool has a diameter of 36 ft and sides that are 6 ft high, and the
depth of the water is 5 ft. Find the work required to pump the water out over the side. (Use
the fact that water weighs 62.5 lb per cubic ft. You may leave your answer as a product.
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 Fall '07
 Mikulevicius
 Math, Calculus

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