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the area of the region bounded by the curve y x2 a
Question:
The area of the region bounded by the curve
y
=
x
2
and the line
y
=
16
is:
MHT CET
Updated On:
Jul 27, 2024
(A)
32
3
sq.units
(B)
256
3
sq.units
(C)
64
3
sq.units
(D)
128
3
sq.units
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The Correct Option is
B
Solution and Explanation
Explanation:
Given equation of curves are
y
=
x
2
⋯
(
1
)
y
=
16
⋯
(
2
)
By solving both equation
(
1
)
and
(
2
)
,
x
2
=
16
x
=
4
,
−
4
∴
Points of intersection are
(
4
,
16
)
and
(
−
4
,
16
)
.
From the figure we have,Required Area
=
∫
−
4
4
(
16
−
x
2
)
d
x
By using Integral property,
A
=
2
∫
0
4
(
16
−
x
2
)
d
x
=
2
[
16
x
−
x
3
3
]
0
4
=
2
[
16
x
−
x
3
3
]
0
4
=
2
[
64
−
64
3
]
=
2
×
64
×
2
3
A
=
256
3
sq.unitsHence, the correct option is (B).
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