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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
7
tan
8
(
x
)
+
7
tan
6
(
x
)
−
3
tan
4
(
x
)
−
3
tan
2
(
x
)
f(x) = 7\tan^8(x) + 7\tan^6(x) - 3\tan^4(x) - 3\tan^2(x)
f
(
x
)
=
7
tan
8
(
x
)
+
7
tan
6
(
x
)
−
3
tan
4
(
x
)
−
3
tan
2
(
x
)
for all
x
∈
(
−
π
2
,
π
2
)
x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
x
∈
(
−
2
π
,
2
π
)
. Then the correct expression(s) is are [JEE(Advanced) 2015] (A)
∫
0
π
/
4
x
f
(
x
)
d
x
=
1
12
\int_{0}^{\pi/4} x f(x) dx = \frac{1}{12}
∫
0
π
/4
x
f
(
x
)
d
x
=
12
1
(B)
∫
0
π
/
4
f
(
x
)
d
x
=
0
\int_{0}^{\pi/4} f(x) dx = 0
∫
0
π
/4
f
(
x
)
d
x
=
0
(C)
∫
0
π
/
4
x
f
(
x
)
d
x
=
1
6
\int_{0}^{\pi/4} x f(x) dx = \frac{1}{6}
∫
0
π
/4
x
f
(
x
)
d
x
=
6
1
(D)
∫
0
π
/
4
f
(
x
)
d
x
=
1
\int_{0}^{\pi/4} f(x) dx = 1
∫
0
π
/4
f
(
x
)
d
x
=
1
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