Antiderivatives of e^x, 1/x and trig

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Mixed review: which is ∫ (3x² + 2 cos x) dx, for Esme?

   • x³ + 2 sin x + C
   • 6x − 2 sin x + C
   • x³ − 2 sin x + C
2. 2.

   Mixed review: which is ∫ (eˣ + sin x) dx, for Jun?

   • eˣ⁺¹/(x + 1) − cos x + C
   • eˣ + cos x + C
   • eˣ − cos x + C
3. 3.

   Mixed review: which is ∫ (4/x − sec² x) dx, for Kira?

   • 4 ln|x| − tan x + C
   • −4/x² − 2sec² x tan x + C
   • 4 ln|x| + tan x + C
4. 4.

   Mixed review: which is ∫ (2e^(2x) + 1/x) dx, for Luz?

   • e^(2x + 1)/(2x + 1) + ln|x| + C
   • 4e^(2x) − 1/x² + C
   • e^(2x) + ln|x| + C
5. 5.

   Milo evaluates ∫ from 0 to ln 5 of 3eˣ dx. What is it?

   12
6. 6.

   Noah evaluates ∫ from 0 to ln 9 of 2eˣ dx. What is it?

   16
7. 7.

   Ren evaluates ∫ from 0 to ln 4 of 5eˣ dx. What is it?

   15
8. 8.

   Tala finds the area of one arch: ∫ from 0 to π/4 of 6 sin(4x) dx. What is it?

   3
9. 9.

   Pia finds the area of one arch: ∫ from 0 to π/4 of 10 sin(4x) dx. What is it?

   5
10. 10.

    Ari finds the area of one arch: ∫ from 0 to π/8 of 12 sin(8x) dx. What is it?

    3