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Mathematics
Mathematics
Problem
Let
f
:
(
0
,
∞
)
→
R
f: (0, \infty) \to \mathbb{R}
f
:
(
0
,
∞
)
→
R
and
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
F(x) = \int_{0}^{x} f(t)\,dt
F
(
x
)
=
∫
0
x
f
(
t
)
d
t
. If
F
(
x
2
)
=
x
2
(
1
+
x
)
F(x^2) = x^2(1+x)
F
(
x
2
)
=
x
2
(
1
+
x
)
, then
f
(
4
)
f(4)
f
(
4
)
is equal to a.
5
4
\frac{5}{4}
4
5
b. 7 c. 4 d. 2
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