What is the formula for finding the average value of a function over an interval?

Calculus: Average Value of a Function

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Mathematics
•
11th Grade - University
•
Hard

Jackson Turner
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The product of the function values at the endpoints of the interval
The integral of the function over the interval divided by the length of the interval
The sum of the function values at the endpoints of the interval
The derivative of the function at the midpoint of the interval
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the integral broken into two parts in this problem?
To make the calculation easier
Because the function is piecewise-defined
To avoid complex numbers
To simplify the derivative
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of 1 with respect to x?
x^2
1
x
0
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of e to the negative 4x?
Negative 4e to the negative 4x
e to the negative 4x
4e to the negative 4x
Negative e to the negative 4x divided by 4
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What rule is applied to find the antiderivative of e to the negative 4x?
Power rule
Chain rule
Product rule
Quotient rule
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of cosine of 0?
1
0
-1
2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final expression for the average value of the function?
3 plus 2 cosine of negative 1 plus e to the negative 4 over 4
13/4 minus 2 cosine of negative 1 minus e to the negative 4 over 4
1/2 times 2 plus cosine of negative 1 plus e to the negative 4 over 4
2 minus cosine of negative 1 minus e to the negative 4 over 4
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