Antiderivatives and the power rule

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Jun writes ∫ 8/x⁵ dx = ax⁻⁴ + C. What is a?

   -2
2. 2.

   Kira writes ∫ 12/x⁴ dx = ax⁻³ + C. What is a?

   -4
3. 3.

   Milo rewrites before integrating. Which is ∫ (x³ + x)/x dx?

   • x³/3 + x + C
   • (x⁴/4 + x²/2)/(x²/2) + C
   • x³/3 + x
4. 4.

   Noah rewrites before integrating. Which is ∫ x(x + 2) dx?

   • x³/3 + x²
   • x³/3 + x² + C
   • (x²/2)(x²/2 + 2x) + C
5. 5.

   Ren rewrites before integrating. Which is ∫ (2x + 1)(x − 3) dx?

   • 2x³/3 − 5x²/2 − 3x
   • 2x³/3 − 5x²/2 − 3x + C
   • (x² + x)(x²/2 − 3x) + C
6. 6.

   Zee rewrites before integrating. Which is ∫ (4x⁵ − x²)/x² dx?

   • (2x⁶/3 − x³/3)/(x³/3) + C
   • x⁴ − x + C
   • x⁴ − x
7. 7.

   Tala writes ∫ 6√x dx = a·x^(3/2) + C. What is a?

   4
8. 8.

   Pia writes ∫ 9√x dx = a·x^(3/2) + C. What is a?

   6
9. 9.

   Esme writes ∫ 12√x dx = a·x^(3/2) + C. What is a?

   8
10. 10.

    Jun writes ∫ 15√x dx = a·x^(3/2) + C. What is a?

    10