Exam II and Key
July 19, 2011
MAC 2312
S Hudson
13 (10 points each) Set up each of these problems, by writing down the deﬁnite integrals
that solve them. Show some work, such as a sketch, background formulas, and/or a brief
discussion. But you do not have to evaluate them.
1) Find the arc length of the parametric curve
x
=
t
3
/
3,
y
=
t
2
/
2, with 0
≤
t
≤
1.
2) Find the volume of the solid that results when the region enclosed by
y
=
√
x
,
y
= 0
and
x
= 9 is revolved about the line
x
= 9. State at the start whether you are using disks,
washers or shells. Setup only.
3) A spring exerts a force of 6 N when stretched from its natural length of 4 m to a length
of 4.5 m. Find the work required to stretch the spring 2 m beyond its natural length. [I
do not care much about the units  you can replace N by lbs and m by ft]. Setup only.
4) [10pts] Compute the average value of
f
(
x
) = sin(2
x
) on [
π/
2
,π
].
5) [10pts] Compute
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 Summer '08
 Storfer
 Calculus, Integrals, Shell Method, Formulas, dt, dx, dx ln x3

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