The average value of
y
=
3
x
2
−
2
x
over the interval
[
2
,
4
]
is the area under the curve divided by the width of the interval.
The area under the curve for the interval
(
2
,
4
)
is
XXX
A
=
∫
4
2
(
3
x
2
−
2
x
)
d
x
XXXx
=
∫
4
2
(
3
x
2
)
d
x
−
∫
4
2
(
2
x
)
d
x
XXXx
=
x
3
]
4
2
−
x
2
]
4
2
XXXx
=
(
64
−
8
)
−
(
16
−
4
)
XXXx
=
56
−
12
=
44
The width of the interval
[
2
,
4
]
is
4
−
2
=
2
So the average value of
y
over this interval is
44
2
=
22
