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Mathematics
Mathematics
Problem
Consider the region bounded by
y
=
ln
x
y = \ln x
y
=
ln
x
,
y
=
0
y = 0
y
=
0
,
x
=
1
x = 1
x
=
1
, and
x
=
e
x = e
x
=
e
. The region is revolved about the horizontal line
y
=
2
y = 2
y
=
2
. What is the exact volume of the resulting solid? a)
π
(
e
−
6
)
\pi\,(e - 6)
π
(
e
−
6
)
b)
π
(
3
e
−
2
)
\pi\,(3e - 2)
π
(
3
e
−
2
)
c)
π
(
6
−
e
)
\pi\,(6 - e)
π
(
6
−
e
)
d)
π
(
e
−
2
)
\pi\,(e - 2)
π
(
e
−
2
)
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