Average value and motion with integrals

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari finds the average value of f(x) = 3x² on 0 ≤ x ≤ 2. What is it?

   4
2. 2.

   Bo finds the average value of f(x) = 6x² on 0 ≤ x ≤ 3. What is it?

   18
3. 3.

   Esme finds the average value of f(x) = 3x² on 0 ≤ x ≤ 4. What is it?

   16
4. 4.

   Jun finds the average value of f(x) = 6x² on 0 ≤ x ≤ 2. What is it?

   8
5. 5.

   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?

   21
6. 6.

   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?

   36
7. 7.

   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?

   26
8. 8.

   ∫ from 1 to 7 of f(x) dx = 48. Ren finds the average value of f on that interval. What is it?

   8
9. 9.

   ∫ from 3 to 8 of f(x) dx = −20. Tala finds the average value of f on that interval. What is it?

   -4
10. 10.

    ∫ from −2 to 4 of f(x) dx = 36. Zee finds the average value of f on that interval. What is it?

    6