Antiderivatives and the power rule

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Esme's F(x) = ∫ (6x² − 4x + 5) dx, with C = 0. What is F(2)?

   18
2. 2.

   Jun's F(x) = ∫ (3x² + 2x − 1) dx, with C = 0. What is F(3)?

   33
3. 3.

   Kira's F(x) = ∫ (9x² − 6x + 2) dx, with C = 0. What is F(2)?

   16
4. 4.

   Luz's F(x) = ∫ (12x² + 4x + 7) dx, with C = 0. What is F(1)?

   13
5. 5.

   Milo rewrites 3/√x as a power of x first. Which is ∫ 3/√x dx?

   • 3√x + C
   • −(3/2)x^(−3/2) + C
   • 6√x + C
6. 6.

   Noah rewrites 4/x³ as a power of x first. Which is ∫ 4/x³ dx?

   • −12/x⁴ + C
   • 4/x² + C
   • −2/x² + C
7. 7.

   Ren rewrites x^(2/3) as a power of x first. Which is ∫ x^(2/3) dx?

   • x^(5/3) + C
   • (3/5)x^(5/3) + C
   • (2/3)x^(−1/3) + C
8. 8.

   Which integral needs a rule other than the power rule, for Tala?

   • ∫ x⁻¹ dx
   • ∫ x^(1/2) dx
   • ∫ x⁻² dx
9. 9.

   Which integral needs a rule other than the power rule, for Esme?

   • ∫ (x² + 1)/x² dx
   • ∫ √x(x + 1) dx
   • ∫ (x² + 1)/x dx
10. 10.

    Which integral needs a rule other than the power rule, for Jun?

    • ∫ 2/(3x) dx
    • ∫ 2∛x dx
    • ∫ 2/(3x²) dx