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Mathematics
Mathematics
Problem
Find a function
f
f
f
, continuous for all
x
x
x
(and not zero everywhere) such that
f
2
(
x
)
=
∫
0
x
f
(
t
)
sin
t
2
+
cos
t
d
t
f^2(x) = \int_{0}^{x} \frac{f(t) \sin t}{2 + \cos t} dt
f
2
(
x
)
=
∫
0
x
2
+
c
o
s
t
f
(
t
)
s
i
n
t
d
t
.
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