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Mathematics
Mathematics
Problem
The function
r
r
r
is defined on
[
0
,
6
]
[0,6]
[
0
,
6
]
by
r
(
x
)
=
{
2
,
0
≤
x
<
3
,
−
2
,
3
≤
x
≤
6
r(x)=\begin{cases} 2, & 0\le x<3,\\ -2, & 3\le x\le 6 \end{cases}
r
(
x
)
=
{
2
,
−
2
,
0
≤
x
<
3
,
3
≤
x
≤
6
Without performing any integration, explain in one sentence why the average value of
r
r
r
on
[
0
,
6
]
[0,6]
[
0
,
6
]
is
0
0
0
.
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