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Mathematics
Mathematics
Problem
The region bounded by
x
=
0
x=0
x
=
0
,
x
=
e
y
x=e^{y}
x
=
e
y
, and
0
≤
y
≤
1
0\le y\le 1
0
≤
y
≤
1
is revolved about the vertical line
x
=
3
x=3
x
=
3
. Which of the following expressions gives the exact volume of the solid? a)
π
(
5
+
e
)
\pi\bigl(5+e\bigr)
π
(
5
+
e
)
b)
π
(
6
e
+
1
2
e
2
−
5.5
)
\pi\bigl(6e+\tfrac12e^{2}-5.5\bigr)
π
(
6
e
+
2
1
e
2
−
5.5
)
c)
π
(
6
e
−
1
2
e
2
−
5.5
)
\pi\bigl(6e-\tfrac12e^{2}-5.5\bigr)
π
(
6
e
−
2
1
e
2
−
5.5
)
d)
π
(
24
−
6
e
+
1
2
e
2
)
\pi\bigl(24-6e+\tfrac12e^{2}\bigr)
π
(
24
−
6
e
+
2
1
e
2
)
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