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Byju's Answer
Standard XII
Mathematics
Area between x=g(y) and y Axis
Find the area...
Question
Find the area of the region bounded by the curve
y
2
=
4
x
and
x
=
3
?
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Solution
Let AB represents the line
x
=
3
and AOB represent the curve
y
2
=
4
x
.
Area of AOBC =
2
×
a
r
(
A
O
C
)
=
2
×
3
∫
0
y
d
x
We know,
y
=
4
x
y
=
±
2
√
x
As AOC is in 1st quadrant,
y
=
2
√
x
Therefore, area of AOBC =
2
×
3
∫
0
2
√
x
d
x
=
4
3
∫
0
√
x
d
x
=
8
3
[
3
3
/
2
−
0
]
=
8
√
3
Therefore, required area =
8
√
3
s
q
.
u
n
i
t
s
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Similar questions
Q.
Find the area of the region bounded by the curve
y
2
= 4
x
and the line
x
= 3