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Mathematics
Mathematics
Problem
Find a continuous function
f
f
f
,
(
x
4
−
4
x
2
)
≤
f
(
x
)
≤
(
2
x
2
−
x
3
)
(x^4 - 4x^2) \le f(x) \le (2x^2 - x^3)
(
x
4
−
4
x
2
)
≤
f
(
x
)
≤
(
2
x
2
−
x
3
)
such that the area bounded by
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
,
y
=
x
4
−
4
x
2
y = x^4 - 4x^2
y
=
x
4
−
4
x
2
, the
Y
Y
Y
-axis and the line
x
=
t
x = t
x
=
t
,
(
0
≤
t
≤
2
)
(0 \le t \le 2)
(
0
≤
t
≤
2
)
is
k
k
k
times the area bounded by
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
,
y
=
2
x
2
−
x
3
y = 2x^2 - x^3
y
=
2
x
2
−
x
3
, the
Y
Y
Y
-axis and the line
x
=
t
x = t
x
=
t
,
(
0
≤
t
≤
2
)
(0 \le t \le 2)
(
0
≤
t
≤
2
)
.
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