find the mean value of f(x) = x2 + 5 on [0, 5]
Answers
Answered by
0
Answer:
The average value is
=
1
Explanation:
The average value of a function
f
(
x
)
over an interval
[
a
,
b
]
is
¯
x
=
1
b
−
a
∫
b
a
f
(
x
)
d
x
Here,
f
(
x
)
=
(
x
−
3
)
2
=
x
2
−
6
x
+
9
and
[
a
,
b
]
=
[
2
,
5
]
Therefore,
¯
x
=
1
5
−
2
∫
5
2
(
x
−
3
)
2
d
x
=
1
3
∫
5
2
(
x
2
−
6
x
+
9
)
d
x
=
1
3
[
x
3
3
−
6
x
2
2
+
9
x
]
5
2
=
1
3
(
(
125
3
−
75
+
45
)
−
(
8
3
−
12
+
18
)
)
=
1
3
(
117
3
−
36
)
=
1
3
⋅
3
=
1
Similar questions