Find the value of the function y=e3x+x=2

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

=
∫
4
2
(
3
x
2
)
d
x
−
∫
4
2
(
2
x
)
d
x

=
x
3
]
4
2
−
x
2
]
4
2

=
(
64
−
8
)
−
(
16
−
4
)

=
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

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

the answer is 18.