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48.
Use the intersect function on a graphing calculator to
determine that the curves intersect at
x
56
1.8933. A shell
has radius
x
and height 3
1
2
x
2
2 }
x
2
1
2
0
3
}
. The volume, which
is calculated using the
right half
of the area, is
E
1.8933
0
2
p
(
x
)
1
3
1
2
x
2
2 }
x
2
1
2
0
3
}
2
dx
, which using NINT
evaluates to
<
9.7717.
49. (a)
y
52}
5
4
}
(
x
1
2)(
x
2
2)
5
5
2 }
5
4
}
x
2
(b)
Revolve about the line
x
5
4, using cylindrical shells.
A shell has radius 4
2
x
and height 5
2 }
5
4
}
x
2
. The total
volume is
E
2
2
2
2
p
(4
2
x
)
1
5
2 }
5
4
}
x
2
2
dx
5
10
p
E
2
2
2
1
}
1
4
}
x
3
2
x
2
2
x
1
4
2
dx
5
10
p
3
}
1
1
6
}
x
4
2 }
1
3
}
x
3
2 }
1
2
}
x
2
1
4
x
4
5 }
32
3
0
}
p
<
335.1032 in
3
.
50.
Since
}
d
d
L
x
} 5 }
1
x
}
1
f
9
(
x
) must equal
ˇ
1
w
1
w
(
w
f
9
w
(
x
w
))
w
2
w
,
1
1
(
f
9
(
x
))
2
5 }
x
1
2
} 1 }
2
x
}
f
9
(
x
)
1
(
f
9
(
x
))
2
, and
f
9
(
x
)
5 }
1
2
}
x
2 }
2
1
x
}
. Then
f
(
x
)
5 }
1
4
}
x
2
2 }
1
2
}
ln
x
1
C
, and the
requirement to pass through (1, 1) means that
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 Spring '08
 GERMAN

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