
Exploring Definite Integrals and Riemann Sums in AP Calculus

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned

Sophia Harris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the function F(T) represent in the context of the problem?
Time in seconds since pumping began
Total amount of gasoline pumped
Rate of flow of gasoline in gallons per second
Cost of gasoline per gallon
Tags
CCSS.HSF.LE.B.5
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the integral from 60 to 135 seconds represent?
Average rate of gasoline flow
Total amount of gasoline pumped in gallons
Total time spent pumping
Total cost of gasoline
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the approximation of the integral from 60 to 135 seconds calculated?
Using exact integration
Using a right Riemann sum
Using a midpoint Riemann sum
Using a left Riemann sum
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical method is used to approximate the integral from 60 to 135 seconds?
Numerical approximation
Algebraic manipulation
Indefinite integration
Definite integration
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
According to the Mean Value Theorem, must there exist a value C between 60 and 120 seconds where F'(C) equals zero?
Yes, because the function is not differentiable at those points
No, because the function is not continuous
No, because the function values at 60 and 120 seconds are different
Yes, because the function values at 60 and 120 seconds are the same
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the Mean Value Theorem applicable in finding a value C between 60 and 120 seconds?
Because the function values at 60 and 120 seconds are different
Because the function is not differentiable in that interval
Because the function is not continuous in that interval
Because the function is continuous and differentiable in that interval
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the average rate of flow of gasoline using the model G(T) from 0 to 150 seconds?
0.096 gallons per second
0.150 gallons per second
0.500 gallons per second
1.50 gallons per second
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