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JEE Main Math Class 12 Application of Integrals Questions
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© examsnet.com
Question : 24
Total: 78
Consider a region
R
=
(
x
,
y
)
∈
{
R
2
:
x
2
≤
y
≤
2
x
}
.
If a line
y
=
α
divides the area of region
R
into two equal parts, then which of the following is true?
[Sep.02,2020(II)]
α
3
−
6
α
2
+
16
=
0
3
α
2
−
8
α
3
∕
2
+
8
=
0
3
α
2
−
8
α
+
8
=
0
α
3
−
6
α
3
∕
2
−
16
=
0
Validate
Solution:
Let
y
=
x
2
and
y
=
2
x
According to question
∴
α
∫
0
(
√
y
−
y
2
)
d
y
=
∫
α
4
(
√
y
−
y
2
)
d
y
⇒
[
y
3
2
3
2
]
0
α
−
[
y
2
4
]
0
α
=
[
y
3
2
3
2
]
α
4
−
[
y
2
4
]
a
4
⇒
2
3
α
3
∕
2
−
α
2
4
=
2
3
(
8
−
α
3
∕
2
)
−
1
4
(
16
−
α
2
)
⇒
4
3
α
3
∕
2
−
α
2
2
=
4
3
⇒
8
α
3
∕
2
−
3
α
2
=
8
∴
3
α
2
−
8
α
3
∕
2
+
8
=
0
© examsnet.com
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