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KVPY SX SB Exam 05-Nov-2017 Question Paper
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© examsnet.com
Question : 8
Total: 120
The parabola
y
2
=
4
x
+
1
divides the disc
x
2
+
y
2
≤
1
into two regions with areas
A
1
and
A
2
. Then
|
A
1
−
A
2
|
equals
1
3
2
3
π
4
π
3
Validate
Solution:
A
1
=
2
0
∫
−
1
∕
4
√
4
x
+
1
d
x
+
2
1
∫
0
√
1
−
x
2
d
x
Solve
A
1
=
1
3
+
π
2
A
2
=
π
(
1
)
2
−
A
1
=
π
2
−
1
3
|
A
1
−
A
2
|
=
2
3
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