Antiderivatives of e^x, 1/x and trig

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Esme writes ∫ 6e^(3x) dx = a·e^(3x) + C. What is a?

   2
2. 2.

   Jun writes ∫ 10e^(2x) dx = a·e^(2x) + C. What is a?

   5
3. 3.

   Kira writes ∫ 12e^(4x) dx = a·e^(4x) + C. What is a?

   3
4. 4.

   Which is ∫ cos x dx, for Milo's sheet?

   • sin x
   • −sin x + C
   • sin x + C
5. 5.

   Which is ∫ sec² x dx, for Ren's sheet?

   • −tan x + C
   • 2sec² x tan x + C
   • tan x + C
6. 6.

   Which is ∫ csc² x dx, for Zee's sheet?

   • cot x + C
   • −2csc² x cot x + C
   • −cot x + C
7. 7.

   Tala evaluates ∫ from 1 to e² of (3/x) dx. What is it?

   6
8. 8.

   Pia evaluates ∫ from 1 to e³ of (5/x) dx. What is it?

   15
9. 9.

   Bo evaluates ∫ from 1 to e⁴ of (2/x) dx. What is it?

   8
10. 10.

    Ari evaluates ∫ from 1 to e² of (6/x) dx. What is it?

    12