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Mathematics
Mathematics
Problem
Let
f
(
x
)
f(x)
f
(
x
)
be a continuous functions for all
x
x
x
, such that
(
f
(
x
)
)
2
=
∫
0
x
f
(
t
)
⋅
2
sec
2
t
4
+
tan
t
d
t
(f(x))^2 = \int_{0}^{x} f(t) \cdot \frac{2 \sec^2 t}{4 + \tan t} dt
(
f
(
x
)
)
2
=
∫
0
x
f
(
t
)
⋅
4
+
t
a
n
t
2
s
e
c
2
t
d
t
and
f
(
0
)
=
0
f(0) = 0
f
(
0
)
=
0
, then a.
f
(
π
4
)
=
log
5
4
f\left(\frac{\pi}{4}\right) = \log \frac{5}{4}
f
(
4
π
)
=
lo
g
4
5
b.
f
(
π
4
)
=
3
4
f\left(\frac{\pi}{4}\right) = \frac{3}{4}
f
(
4
π
)
=
4
3
c.
f
(
π
2
)
=
2
f\left(\frac{\pi}{2}\right) = 2
f
(
2
π
)
=
2
d. None of these
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