Average Value of Functions on Intervals
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the average value of
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
on the interval
[
0
,
2
]
[0, 2]
[
0
,
2
]
?
QUESTION
What is the average value of
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
on
[
1
,
2
]
[1, 2]
[
1
,
2
]
?
QUESTION
What is the average value of
f
(
x
)
=
2
x
+
3
f(x) = 2x + 3
f
(
x
)
=
2
x
+
3
on
[
0
,
4
]
[0, 4]
[
0
,
4
]
?
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ANSWER
7
7
7
. Apply the formula:
1
4
∫
0
4
(
2
x
+
3
)
d
x
=
1
4
⋅
28
=
7
\frac{1}{4}\int_0^4 (2x+3)\,dx = \frac{1}{4} \cdot 28 = 7
4
1
∫
0
4
(
2
x
+
3
)
d
x
=
4
1
⋅
28
=
7
.
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