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Mathematics
Mathematics
Problem
Let
h
(
x
)
=
{
x
+
1
,
0
≤
x
<
2
,
k
x
2
,
2
≤
x
≤
4
h(x)=\begin{cases} x+1, & 0\le x<2,\\ kx^{2}, & 2\le x\le 4 \end{cases}
h
(
x
)
=
{
x
+
1
,
k
x
2
,
0
≤
x
<
2
,
2
≤
x
≤
4
Find the constant
k
k
k
so that the average value of
h
h
h
on
[
0
,
4
]
[0,4]
[
0
,
4
]
equals
5
5
5
.
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