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Solved Examples
Curriculum:
Alaska Math Grade Level Expectations
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Topic:
Applications of Integration
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Lesson:
Average Value of a Function
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Attempt following question by selecting a choice to answer.
e
Which of the following is the average value of
y
=
e
x
+ 2
x
on
[0, 1]?
DD ee
A.
e
e
B.
e
e
+ 3
C.
e
e
+ 2
D.
e
e
+ 1
E.
e
-
e
e
A
View Solution Steps
Step 1:
y
=
e
x
+ 2
x
[Write the function.]
Step 2: The average value of
y
on [0, 1] is
y
¯
=
1
1
-
0
∫
0
1
(
e
x
+ 2
x
)
dx
[Use
1
b
-
a
∫
a
b
y
dx
]
Step 3: =
∫
0
1
(
e
x
+ 2
x
)
dx
Step 4: = (
e
x
+
2
x
2
2
)
0
1
[Integrate.]
Step 5: = [(
e
+ 1) - (
e
0
+ 0)][Apply the limits.]
Step 6: =
e
+ 1 - 1 =
e
[Simplify.]
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