Grade 12 · Math · Calculus

12th grade Average value and motion with integrals worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Average value and motion with integrals

Grade 12 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Ari finds the average value of f(x) = 3x² on 0 ≤ x ≤ 2. What is it?
Bo finds the average value of f(x) = 6x² on 0 ≤ x ≤ 3. What is it?
Esme finds the average value of f(x) = 3x² on 0 ≤ x ≤ 4. What is it?
Jun finds the average value of f(x) = 6x² on 0 ≤ x ≤ 2. What is it?
A toy cart has velocity v(t) = 4t + 1 m/s, never negative for 0 ≤ t ≤ 3. Kira finds how far it moves. What is it, in meters?
A robot has velocity v(t) = 2t + 5 m/s, never negative for 0 ≤ t ≤ 4. Luz finds how far it moves. What is it, in meters?
A toy train has velocity v(t) = 10t + 3 m/s, never negative for 0 ≤ t ≤ 2. Noah finds how far it moves. What is it, in meters?
∫ from 1 to 7 of f(x) dx = 48. Ren finds the average value of f on that interval. What is it?
∫ from 3 to 8 of f(x) dx = −20. Tala finds the average value of f on that interval. What is it?
∫ from −2 to 4 of f(x) dx = 36. Zee finds the average value of f on that interval. What is it?

Average value and motion with integrals. Every version has 10 questions, and the answer key prints on the second page.

I can find the average value of a function on an interval.
I can find displacement and total distance from a velocity.
I can work back from an average to the interval, and write the integral for distance.

Standard: none (beyond CCSS)

average value: (1/(b − a)) ∫ from a to b of f(x) dx.

displacement: ∫ v dt: the change in position.

Gave the integral instead of the average. The average value is the integral divided by the interval's width.

Averaged the two end values. The average value uses every value, through the integral.

Gave the final velocity instead of the distance. Distance is the integral of speed over time.

What is the most common mistake with average value and motion with integrals?

Gave the integral instead of the average. The average value is the integral divided by the interval's width.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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