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Mathematics
If the area bounded by the parabola y=2-x2 and the line y=-x is (k/2) sq. units, then the value of 2k is equal to
Q. If the area bounded by the parabola
y
=
2
−
x
2
and the line
y
=
−
x
is
2
k
sq. units, then the value of
2
k
is equal to
1058
152
NTA Abhyas
NTA Abhyas 2020
Application of Integrals
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A
9
12%
B
27
12%
C
18
67%
D
32
8%
Solution:
Solving
y
=
2
−
x
2
&
y
=
−
x
;
we get
−
x
=
2
−
x
2
⇒
x
=
2
,
−
1
⇒
A
(
−
1
,
1
)
&
B
(
2
,
−
2
)
Thus, the required area
A
=
−
1
∫
2
(
2
−
x
2
)
−
(
−
x
)
d
x
=
[
2
x
−
3
x
3
+
2
x
2
]
−
1
2
=
2
9
⇒
k
=
9
∴
2
k
=
18