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NDA Math Conic Section
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© examsnet.com
Question : 11
Total: 34
What is the area of the region enclosed between the curve
y
2
=
2
x
and the straight line
y
=
x
?
[NDA-I 2020]
1
2
1
2
3
2
Validate
Solution:
👈: Video Solution
Two given graphs are
y
2
=
2
x
and
y
=
x
.
Point of intersections are :
x
2
=
2
x
⇒
x
2
−
2
x
=
0
x
(
x
−
2
)
=
0
x
=
0
and
2
&
y
=
0
and 2
So, points of intersections are (0,0) and (2,2) . The graph are
The required area is the shaded portion
A
=
|
2
∫
0
(
y
1
−
y
2
)
.
d
x
|
=
|
2
∫
0
(
√
2
x
−
x
)
.
d
x
|
=
[
2
√
2
(
x
)
3
2
3
−
x
2
2
]
0
2
=
2
√
2
3
(
2
)
3
2
−
2
=
8
3
−
2
=
2
3
© examsnet.com
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