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NDA Math Area Under the Curves
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© examsnet.com
Question : 15
Total: 27
What is the area bounded by the curves
|
y
|
=
1
−
x
2
?
[NDA II 2016]
4
3
square units
8
3
square units
4 square units
16
3
square units
Validate
Solution:
Since
|
y
|
=
{
y
y
>
0
−
y
y
<
0
0
y
=
0
For
y
>
0
⇒
y
=
1
−
x
2
For
y
<
0
⇒
y
=
x
2
−
1
For
y
=
0
⇒
x
=
±
1
So area under the curve
= 4 × Area under the region OABO (symmetry)
=
4
×
1
∫
0
1
−
x
2
d
x
=
4
×
[
x
−
x
3
3
]
0
1
]
=
4
(
1
−
1
3
)
=
4
×
2
3
=
8
3
sq. units
© examsnet.com
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