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Mathematics
Mathematics
Problem
Evaluate the average value of the function
p
(
x
)
=
{
1
,
0
≤
x
<
1
,
3
,
x
=
1
,
1
+
(
x
−
1
)
2
,
1
<
x
≤
3
p(x)=\begin{cases} 1, & 0\le x<1,\\ 3, & x=1,\\ 1+(x-1)^{2}, & 1< x\le 3 \end{cases}
p
(
x
)
=
⎩
⎨
⎧
1
,
3
,
1
+
(
x
−
1
)
2
,
0
≤
x
<
1
,
x
=
1
,
1
<
x
≤
3
on the interval
[
0
,
3
]
[0,3]
[
0
,
3
]
.
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