Antiderivatives and the power rule

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Jun writes ∫ 8x³ dx = ax⁴ + C. What is a?

   2
2. 2.

   Kira writes ∫ 21x⁶ dx = ax⁷ + C. What is a?

   3
3. 3.

   Luz writes ∫ 35x⁴ dx = ax⁵ + C. What is a?

   7
4. 4.

   Which is ∫ (4x³ + 6x) dx, for Milo's sheet?

   • x⁴ + 3x² + C
   • x⁴ + 3x²
   • 4x⁴ + 6x² + C
5. 5.

   Which is ∫ (9x² − 2) dx, for Noah's sheet?

   • 3x³ − 2x + C
   • 3x³ − 2x
   • 9x³ − 2x + C
6. 6.

   Which is ∫ (1/x²) dx, for Ren's sheet?

   • −1/x
   • −1/x + C
   • −2/x³ + C
7. 7.

   Tala's F has F′(x) = 4x³ + 6x and F(0) = 0. What is F(2)?

   28
8. 8.

   Pia's F has F′(x) = 4x³ + 6x and F(0) = 0. What is F(3)?

   108
9. 9.

   Esme's F has F′(x) = 4x³ + 6x and F(0) = 0. What is F(1.5)?

   11.8125
10. 10.

    Jun's F has F′(x) = 4x³ + 6x and F(0) = 0. What is F(4)?

    304