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Mat104 Fall 2002, Problems on Area, Volume and Length From Old Exams
(1) (a) The region
S
bounded by
y
= sec
x
and the
x
axis for

π/
4
≤
x
≤
π/
4 is rotated
around the
x
axis. Find the volume of the resulting solid.
(b) The region
R
bounded by the parabolas
y
2
=
x
and
y
2
= 2
x

6 is rotated about the
x
axis. Find the volume of the resulting solid.
(2) Find the arc length of the of the curve given by
x
=
e
2
t
sin 2
t
,
y
=
e
2
t
cos 2
t
for 0
≤
t
≤
1.
(3) The region enclosed between the curve
y
=
e

x
and the lines
x
= 1 and
x
= 2 is rotated
around the
x
axis. Find the volume of the resulting solid of revolution and the surface area
of the boundary of this solid.
(4) Let
R
be the region above the
x
axis, to the right of the
y
axis, and below the circle of
radius 1 and center (1
,
1). Find the area of
R
. Find the volume of the solid
S
obtained by
rotating the region
R
around the
x
axis. Find the surface area of this solid
S
.
(5) Let
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 Fall '07
 Nelson

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