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Mathematics
Mathematics
Problem
Consider the curve defined implicitly by
2
x
y
+
y
2
=
8
2xy + y^{2} = 8
2
x
y
+
y
2
=
8
. Let
S
S
S
be the region bounded by this curve, the
y
y
y
-axis, and the horizontal lines
y
=
1
y=1
y
=
1
and
y
=
2
y=2
y
=
2
. Which of the following is the exact area of
S
S
S
? a)
4
ln
2
+
3
4
4\ln 2 + \dfrac{3}{4}
4
ln
2
+
4
3
b)
4
ln
2
−
3
2
4\ln 2 - \dfrac{3}{2}
4
ln
2
−
2
3
c)
4
ln
2
−
3
4
4\ln 2 - \dfrac{3}{4}
4
ln
2
−
4
3
d)
2
ln
2
−
3
4
2\ln 2 - \dfrac{3}{4}
2
ln
2
−
4
3
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