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.

   Esme writes ∫ 15x² dx = ax³ + C. What is a?

   5
2. 2.

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

   2
3. 3.

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

   3
4. 4.

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

   7
5. 5.

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

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

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

   • 3x³ − 2x + C
   • 9x³ − 2x + C
   • 3x³ − 2x
7. 7.

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

   • −1/x
   • −2/x³ + C
   • −1/x + C
8. 8.

   Which is ∫ (√x) dx, for Zee's sheet?

   • (2/3)x^(3/2)
   • (1/2)x^(−1/2) + C
   • (2/3)x^(3/2) + C
9. 9.

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

   108
10. 10.

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

    304