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KCET 2016 Math Solved Paper
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© examsnet.com
Question : 20
Total: 60
The value of
π
∕
4
∫
−
π
∕
4
s
i
n
103
x
.
c
o
s
101
x
dx
is
(
π
4
)
103
(
π
4
)
101
2
0
Validate
Solution:
Given that
π
4
∫
−
π
4
sin
103
x
⋅
cos
101
x
d
x
Let
f
(
x
)
=
sin
103
x
cos
101
x
Then
f
(
−
x
)
=
sin
103
(
−
x
)
cos
101
(
−
x
)
=
−
sin
103
x
cos
101
x
=
−
f
(
x
)
So, it is an odd function.
Since,
a
∫
−
a
f
(
x
)
d
x
=
0
Therefore
π
4
∫
−
π
4
sin
103
x
⋅
cos
101
x
d
x
=
0
© examsnet.com
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