Antiderivatives of e^x, 1/x and trig

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Esme evaluates ∫ from π/6 to π/2 of 8 cos x dx. What is it?

   4
2. 2.

   Jun evaluates ∫ from π/6 to π/2 of 10 cos x dx. What is it?

   5
3. 3.

   Kira evaluates ∫ from π/2 to π/6 of 3 cos x dx. What is it?

   -3/2
4. 4.

   Luz evaluates ∫ from π/6 to π/2 of 7 cos x dx. What is it?

   7/2
5. 5.

   Which is ∫ (2eˣ + 3/x) dx, for Milo?

   • 2eˣ⁺¹/(x + 1) + 3 ln|x| + C
   • 2eˣ − 3/x² + C
   • 2eˣ + 3 ln|x| + C
6. 6.

   Which is ∫ (e^(4x)) dx, for Noah?

   • (1/4)e^(4x) + C
   • e^(4x + 1)/(4x + 1) + C
   • 4e^(4x) + C
7. 7.

   Which is ∫ (eˣ − 4/x) dx, for Ren?

   • eˣ + 4/x² + C
   • eˣ − 4 ln|x| + C
   • eˣ⁺¹/(x + 1) − 4 ln|x| + C
8. 8.

   Which is ∫ (6e^(2x)) dx, for Zee?

   • 6e^(2x + 1)/(2x + 1) + C
   • 12e^(2x) + C
   • 3e^(2x) + C
9. 9.

   Bo writes ∫ 9 cos(2x) dx = a·sin(2x) + C. What is a?

   9/2
10. 10.

    Ari writes ∫ 12 cos(3x) dx = a·sin(3x) + C. What is a?

    4