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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a function defined by
f
(
x
)
=
{
[
x
]
,
x
≤
2
0
,
x
>
2
f(x) = \begin{cases} [x], & x \le 2 \\ 0, & x > 2 \end{cases}
f
(
x
)
=
{
[
x
]
,
0
,
x
≤
2
x
>
2
, where
[
x
]
[x]
[
x
]
is the greatest integer less than or equal to
x
x
x
. If
I
=
∫
−
1
2
x
f
(
x
2
)
2
+
f
(
x
+
1
)
d
x
I = \int_{-1}^{2} \frac{x f(x^2)}{2 + f(x+1)} dx
I
=
∫
−
1
2
2
+
f
(
x
+
1
)
x
f
(
x
2
)
d
x
, then the value of
(
4
I
−
1
)
(4I-1)
(
4
I
−
1
)
is
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