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Mathematics
Mathematics
Problem
If the area of the bounded region
R
=
{
(
x
,
y
)
:
max
{
0
,
log
e
x
}
≤
y
≤
2
x
,
1
2
≤
x
≤
2
}
R = \left\{ (x, y) : \max\{0, \log_e x\} \le y \le 2^x, \frac{1}{2} \le x \le 2 \right\}
R
=
{
(
x
,
y
)
:
max
{
0
,
lo
g
e
x
}
≤
y
≤
2
x
,
2
1
≤
x
≤
2
}
is,
α
(
log
e
2
)
−
1
+
β
(
log
e
2
)
+
γ
\alpha(\log_e 2)^{-1} + \beta(\log_e 2) + \gamma
α
(
lo
g
e
2
)
−
1
+
β
(
lo
g
e
2
)
+
γ
, then the value of
(
α
+
β
−
2
γ
)
2
(\alpha + \beta - 2\gamma)^2
(
α
+
β
−
2
γ
)
2
is equal to : (A) 8 (B) 2 (C) 4 (D) 1
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