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Byju's Answer
Standard XII
Mathematics
Area between Two Curves
Find the area...
Question
Find the area of the region bounded by the two parabolas
y
=
x
2
and
y
2
=
x
.
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Solution
The given curves are
y
=
x
2
and
y
2
=
x
i.e.
y
=
√
x
To find the intersection point of two curves, let us have
x
2
=
√
x
⟹
x
4
=
x
⟹
x
4
−
x
=
0
⟹
x
(
x
3
−
1
)
=
0
⟹
x
=
0
and
x
=
1
⟹
(
0
,
0
)
and
(
1
,
1
)
are the points of intersection of two curves.
∴
Area bounded by these two curves
=
∫
1
0
(
x
2
−
√
x
)
d
x
=
∣
∣ ∣
∣
x
3
3
−
(
x
)
3
2
3
2
∣
∣ ∣
∣
1
0
=
1
3
−
2
3
=
−
1
3
Hence, area bounded by two parabolas
y
=
x
2
and
y
2
=
x
is
−
1
3
.
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y
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