Average value and motion with integrals

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   The average value of f(x) = 3x² on 0 ≤ x ≤ b is 16. Ari solves for b > 0. What is b?

   4
2. 2.

   The average value of f(x) = 3x² on 0 ≤ x ≤ b is 25. Bo solves for b > 0. What is b?

   5
3. 3.

   The average value of f(x) = 3x² on 0 ≤ x ≤ b is 36. Esme solves for b > 0. What is b?

   6
4. 4.

   The average value of f(x) = 3x² on 0 ≤ x ≤ b is 49. Jun solves for b > 0. What is b?

   7
5. 5.

   A sled has velocity v(t) = (t − 1)(t − 4) m/s for 0 ≤ t ≤ 5. Kira finds the total distance. What is it, to the nearest hundredth?

   8.17
6. 6.

   A toy train has velocity v(t) = (t − 1)(t − 5) m/s for 0 ≤ t ≤ 6. Luz finds the total distance. What is it, to the nearest hundredth?

   15.33
7. 7.

   A robot has velocity v(t) = (t − 1)(t − 5) m/s for 0 ≤ t ≤ 7. Noah finds the total distance. What is it, to the nearest hundredth?

   23.67
8. 8.

   Pia wants the total distance for v(t) = t − 2 on 0 ≤ t ≤ 5. Which expression gives it?

   • ∫ from 0 to 5 of (t − 2) dt
   • |∫ from 0 to 5 of (t − 2) dt|
   • ∫ from 0 to 2 of (2 − t) dt + ∫ from 2 to 5 of (t − 2) dt
   • ∫ from 0 to 2 of (t − 2) dt + ∫ from 2 to 5 of (t − 2) dt
9. 9.

   Ren wants the total distance for v(t) = 3 − t on 1 ≤ t ≤ 6. Which expression gives it?

   • ∫ from 1 to 3 of (3 − t) dt + ∫ from 3 to 6 of (t − 3) dt
   • ∫ from 1 to 3 of (3 − t) dt + ∫ from 3 to 6 of (3 − t) dt
   • |∫ from 1 to 6 of (3 − t) dt|
   • ∫ from 1 to 6 of (3 − t) dt
10. 10.

    Zee wants the total distance for v(t) = t − 4 on 1 ≤ t ≤ 7. Which expression gives it?

    • ∫ from 1 to 4 of (4 − t) dt + ∫ from 4 to 7 of (t − 4) dt
    • ∫ from 1 to 7 of (t − 4) dt
    • ∫ from 1 to 4 of (t − 4) dt + ∫ from 4 to 7 of (t − 4) dt
    • |∫ from 1 to 7 of (t − 4) dt|