Calculus 2 Practice Test

Name: ______________________   Date: __________   Score: ____ / 40

40 questions. Calculator allowed. Show your working. steplyclass.com/calculus-2/practice-test/

1. 1

   Integrate ∫ e^3x dx

   Answer: ____________________

2. 2

   Evaluate ∫ from 0 to 1 of 6e^3x dx

   Answer: ____________________

3. 3

   Find the volume of y = √x turned around the x-axis from x = 0 to x = 4.
   1. A) V ≈ 25.13
   2. B) V ≈ −25.13
   3. C) V ≈ 251.3
   4. D) V ≈ 25130

4. 4

   Find the volume between y = 5 and y = x² + 1 turned around the x-axis.

   Answer: ____________________

5. 5

   Find the volume of y = x² from x = 0 to x = 2 turned around the y-axis.
   1. A) V ≈ 251.3
   2. B) V ≈ −25.13
   3. C) V ≈ 25130
   4. D) V ≈ 25.13

6. 6

   Find the volume of y = 1 − x² from x = 0 to x = 1 turned around the y-axis.

   Answer: ____________________

7. 7

   Find the length of y = 34x from x = 0 to x = 4.

   Answer: ____________________

8. 8

   Find the length of y = x⁴8 + 1/(4x²) from x = 1 to x = 3.

   Answer: ____________________

9. 9

   Find the surface area of y = 34x turned around the x-axis from x = 0 to x = 4.
   1. A) S ≈ 4.712
   2. B) S ≈ 47.12
   3. C) S ≈ −47.12
   4. D) S ≈ 471.2

10. 10

    Find the surface area of y = x³3 turned around the x-axis from x = 0 to x = 2.

    Answer: ____________________

11. 11

    Integrate ∫ x e^x dx

    Answer: ____________________

12. 12

    Evaluate ∫ from 0 to 2 of x e^x dx
    1. A) 8.389
    2. B) 0.8389
    3. C) 8389
    4. D) 83.89

13. 13

    Evaluate ∫ from 0 to π of sin² x dx
    1. A) 0.157
    2. B) 1.57
    3. C) 15.7
    4. D) 1570

14. 14

    Evaluate ∫ from 0 to π of sin³ x dx

    Answer: ____________________

15. 15

    Integrate ∫ 1/(x²√(4 − x²)) dx

    Answer: ____________________

16. 16

    Evaluate ∫ from 0 to 4 of √(16 − x²) dx

    Answer: ____________________

17. 17

    Evaluate ∫ from 2 to 4 of 1/(x² − 1) dx
    1. A) 0.0294
    2. B) 0.294
    3. C) 1
    4. D) 2.94

18. 18

    Evaluate ∫ from 1 to 2 of 3/(x² + 3x) dx
    1. A) 3
    2. B) 4.7
    3. C) 0.470
    4. D) 1

19. 19

    Evaluate ∫ from 1 to ∞ of 1x² dx

    Answer: ____________________

20. 20

    Evaluate ∫ from 0 to ∞ of 4e^−2x dx

    Answer: ____________________

21. 21

    Find the limit of the sequence a_n = 5n^2.
    1. A) Converges
    2. B) Diverges

22. 22

    Find the limit of the sequence a_n = n³ − 2n4n³ + 1.
    1. A) Converges
    2. B) Diverges

23. 23

    Does Σ n/(2n + 1) converge
    1. A) Converges
    2. B) Diverges

24. 24

    Does Σ (−1)ⁿ n² + 12n² converge
    1. A) Converges
    2. B) Diverges

25. 25

    Does Σ 1n² converge
    1. A) Converges
    2. B) Diverges

26. 26

    Use the integral test on Σ 1n^2/3
    1. A) Converges
    2. B) Diverges

27. 27

    Does Σ 1/(n² + 3) converge
    1. A) Converges
    2. B) Diverges

28. 28

    Does Σ 3n − 1n³ + 1 converge
    1. A) Converges
    2. B) Diverges

29. 29

    Does Σ (−1)ⁿ⁺¹/n converge
    1. A) Converges
    2. B) Diverges

30. 30

    Does Σ (−1)ⁿ 45ⁿ converge
    1. A) Converges
    2. B) Diverges

31. 31

    Does Σ 2ⁿn! converge
    1. A) Converges
    2. B) Diverges

32. 32

    Does Σ (2n + 15n + 3)ⁿ converge
    1. A) Converges
    2. B) Diverges

33. 33

    Interval of convergence of Σ (x − 2)ⁿ/3ⁿ

    Answer: ____________________

34. 34

    Interval of convergence of Σ n!(x − 1)ⁿ

    Answer: ____________________

35. 35

    Maclaurin polynomial of degree 3 for e^x

    Answer: ____________________

36. 36

    Maclaurin polynomial of degree 4 for e^−2x

    Answer: ____________________

37. 37

    x = t², y = t³, find dy/dx

    Answer: ____________________

38. 38

    x = t² − 2t, y = t³, find the slope at t = 2

    Answer: ____________________

39. 39

    Find the area inside r = 3.
    1. A) A ≈ 28.27
    2. B) A ≈ 282.7
    3. C) A ≈ 56.54
    4. D) 18π

40. 40

    Find the area inside r = 4 + 2sin θ.

    Answer: ____________________