Practice Test IV C for Math 1501, Calculus I
Problem 1:
Let Ω be the region in the
x, y
plane bounded by:
y
=
x
4
y
= 4
x
2
(a) Find the area of this region.
(b) Find the centroid of this region.
(c) Find the volume of the body produced by rotating this region about the line
x
= 0.
(d) Find the volume of the body produced by rotating this region about the line
x
= 3.
Problem 2:
a) A flagpole that is 10 m long, that has a uniform mass density of 1
kg/m
is initially lying down and is stood up on its end. How much work is done?
b) Now suppose that the flagpole is tapered with a mass density
ρ
(
x
) = 2

x
10
kg
/
m
,
where
x
is the distance from the base. How much work is done in raising the flagpole this
time?
Problem 3:
A doughnut whose precise dimension is given below, is covered by a layer of
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 Fall '08
 N/A
 Calculus, mass density, xn e−x dx

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