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Question
Mathematics
The area bounded the curve y2 = 16x and line y =mx is (2/3), then m is equal to
Q. The area bounded the curve
y
2
=
16
x
and line
y
=
m
x
is
3
2
, then
m
is equal to
5643
210
Application of Integrals
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A
3
12%
B
4
63%
C
1
17%
D
2
7%
Solution:
We have,
y
2
=
16
x
, a parabola with vertex
(
0
,
0
)
and line
y
=
m
x
.
Required area = area of shaded region
=
0
∫
16
m
2
(
16
x
−
m
x
)
d
x
=
3
2
⇒
[
4
×
3
2
x
2
3
−
m
(
2
x
2
)
]
0
m
2
16
=
3
2
⇒
3
8
×
m
3
64
−
2
m
m
4
256
=
3
2
⇒
m
3
1
[
3
512
−
128
]
=
3
2
⇒
m
=
4