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Mathematics
Mathematics
Problem
A solid is formed by revolving the region bounded by the graph of
y
=
x
+
1
x
+
3
y=\dfrac{x+1}{x+3}
y
=
x
+
3
x
+
1
, the
x
x
x
–axis, and the vertical lines
x
=
0
x=0
x
=
0
and
x
=
2
x=2
x
=
2
about the
y
y
y
–axis. What is the exact volume of this solid? a)
2
π
(
6
ln
5
3
)
2\pi\bigl(6\ln\dfrac{5}{3}\bigr)
2
π
(
6
ln
3
5
)
b)
2
π
(
2
+
6
ln
5
3
)
2\pi\bigl(2+6\ln\dfrac{5}{3}\bigr)
2
π
(
2
+
6
ln
3
5
)
c)
2
π
(
−
2
+
6
ln
5
3
)
2\pi\bigl(-2+6\ln\dfrac{5}{3}\bigr)
2
π
(
−
2
+
6
ln
3
5
)
d)
π
(
−
2
+
6
ln
5
3
)
\pi\bigl(-2+6\ln\dfrac{5}{3}\bigr)
π
(
−
2
+
6
ln
3
5
)
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