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UPSC NDA Math Model Paper 2
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© examsnet.com
Question : 74
Total: 120
The value of
2
∫
−
2
(
a
x
5
+
b
x
3
+
c
)
d
x
depends on the value of:
b.
c.
a.
a and b.
Validate
Solution:
We observe that
a
x
5
and
b
x
3
are odd functions of
x
, because
a
(
−
x
)
5
=
−
a
x
5
and
b
(
−
x
)
3
=
−
b
x
3
.
∴
2
∫
−
2
a
x
5
d
x
=
0
and
2
∫
−
2
b
x
3
d
x
=
0
The value of
2
∫
−
2
(
a
x
5
+
b
x
3
+
c
)
d
x
depends on the value of
c
.
In fact,
2
∫
−
2
(
a
x
5
+
b
x
3
+
c
)
d
x
2
∫
−
2
c
d
x
=
c
[
x
]
−
2
2
=
c
[
2
−
(
−
2
)
]
=
4
c
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