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NDA Math Definite Integrals
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© examsnet.com
Question : 30
Total: 62
If
f
(
x
)
and
g
(
x
)
are continuous functions satisfying
f
(
x
)
=
f
(
a
−
x
)
and
g
(
x
)
+
g
(
a
−
x
)
=
2
,then what is
a
∫
0
f
(
x
)
g
(
x
)
d
x
equal to ?
[NDA I 2017]
a
∫
0
g
(
x
)
d
x
a
∫
0
f
(
x
)
d
x
2
a
∫
0
f
(
x
)
d
x
a
∫
0
0
Validate
Solution:
I
=
a
∫
0
f
(
x
)
g
(
x
)
d
x
=
a
∫
0
f
(
a
−
x
)
⋅
g
(
a
−
x
)
d
x
=
a
∫
0
f
(
x
)
{
2
−
g
(
x
)
}
d
x
=
a
∫
0
2
f
(
x
)
d
x
−
a
∫
0
f
(
x
)
⋅
g
(
x
)
d
x
⇒
2
I
=
2
a
∫
0
f
(
x
)
d
x
⇒
I
=
a
∫
0
f
(
x
)
d
x
© examsnet.com
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