Definite integrals and net area

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Kira uses the triangles above and below the axis. What is ∫ from 0 to 7 of (5 − x) dx?

   10.5
2. 2.

   Luz uses the triangles above and below the axis. What is ∫ from 0 to 9 of (6 − x) dx?

   13.5
3. 3.

   Milo knows ∫ from 1 to 7 of f(x) dx = 10 and ∫ from 1 to 3 of f(x) dx = 4. What is ∫ from 3 to 7 of f(x) dx?

   6
4. 4.

   Noah knows ∫ from 0 to 8 of f(x) dx = −5 and ∫ from 0 to 2 of f(x) dx = 6. What is ∫ from 2 to 8 of f(x) dx?

   -11
5. 5.

   Ren knows ∫ from 2 to 9 of f(x) dx = 20 and ∫ from 2 to 5 of f(x) dx = 12. What is ∫ from 5 to 9 of f(x) dx?

   8
6. 6.

   Zee knows ∫ from −1 to 6 of f(x) dx = 7.5 and ∫ from −1 to 3 of f(x) dx = 2.5. What is ∫ from 3 to 6 of f(x) dx?

   5
7. 7.

   Tala knows ∫ from 2 to 5 of f(x) dx = 8. What is ∫ from 5 to 2 of 3f(x) dx?

   -24
8. 8.

   Pia knows ∫ from 0 to 4 of f(x) dx = 5. What is ∫ from 4 to 0 of −2f(x) dx?

   10
9. 9.

   Bo knows ∫ from 1 to 7 of f(x) dx = 12. What is ∫ from 7 to 1 of 0.5f(x) dx?

   -6
10. 10.

    Ari knows ∫ from 3 to 10 of f(x) dx = 9. What is ∫ from 10 to 3 of 4f(x) dx?

    -36