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Byju's Answer
Standard XII
Mathematics
Area between Two Curves
The area encl...
Question
The area enclosed by the parabolas
x
=
−
2
y
2
and
x
=
1
−
3
y
2
is
a
b
,
where
a
,
b
are co-prime. Then
a
+
b
is
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Solution
Point of intersection of the parabolas,
−
2
y
2
=
1
−
3
y
2
⇒
y
=
±
1
⇒
x
=
−
2
So, the required area is,
=
2
1
∫
0
(
1
−
3
y
2
)
−
(
−
2
y
2
)
d
y
=
2
1
∫
0
(
1
−
y
2
)
d
y
=
2
[
y
−
y
3
3
]
1
0
=
2
×
2
3
=
4
3
Hence,
a
+
b
=
7
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