Average Value of Functions on Intervals
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Describe how average value of a function is related to its definite integral.
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
]
?
QUESTION
What is the integral form used to calculate the average value of
f
(
x
)
f(x)
f
(
x
)
on
[
a
,
b
]
[a, b]
[
a
,
b
]
?
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ANSWER
1
b
−
a
×
∫
a
b
f
(
x
)
d
x
\frac{1}{b-a} \times \int_a^b f(x) \, dx
b
−
a
1
×
∫
a
b
f
(
x
)
d
x
. This is the mathematical definition using the fundamental theorem of calculus.
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