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Joint Entrance Examination
Mathematics
Area Under Curves
Question 15
Question 15 of 230
Medium
MCQ
If the area of the region
(
x
,
y
)
:
1
−
2
x
≤
y
≤
4
−
x
2
,
x
≥
0
,
y
≥
0
{(x,y):1-2x\le y\le 4-{x}^{2},\, x\ge 0,\, y\ge 0}
(
x
,
y
)
:
1
−
2
x
≤
y
≤
4
−
x
2
,
x
≥
0
,
y
≥
0
is
α
β
\frac{\alpha }{\beta }
β
α
,
α
,
β
∈
N
,
g
c
d
(
α
,
β
)
=
1
\alpha ,\beta \in N,gcd(\alpha ,\beta )=1
α
,
β
∈
N
,
g
c
d
(
α
,
β
)
=
1
, then the value of
(
α
+
β
)
(\alpha +\beta )
(
α
+
β
)
is:
A
73
B
85
C
67
D
91
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Official solution
∫
2
0
(
4
−
x
2
)
d
x
−
1
2
×
1
×
1
2
{\int }_{2}^{0}(4-{x}^{2})dx-\frac{1}{2}\times 1\times \frac{1}{2}
∫
2
0
(
4
−
x
2
)
d
x
−
2
1
×
1
×
2
1
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