Calculus 2 Practice Test
40 questions from 20 lessons · 120 minutes · percent score and grade · step-by-step answers
How it works
- 40 questions, about 120 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 20 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise these lessons next: the lessons of the questions you got wrong, with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
Formulas: the Calculus 2 formula sheet.
1 Question 1
Integrate ∫ e3x dxType the answer.
2 Question 2
Evaluate ∫ from 0 to 1 of 6e3x dxType the answer.
3 Question 3
Find the volume of y = √x turned around the x-axis from x = 0 to x = 4.- A) V ≈ 25.13
- B) V ≈ −25.13
- C) V ≈ 251.3
- D) V ≈ 25130
4 Question 4
Find the volume between y = 5 and y = x2 + 1 turned around the x-axis.Type the answer.
5 Question 5
Find the volume of y = x2 from x = 0 to x = 2 turned around the y-axis.- A) V ≈ 251.3
- B) V ≈ −25.13
- C) V ≈ 25130
- D) V ≈ 25.13
6 Question 6
Find the volume of y = 1 − x2 from x = 0 to x = 1 turned around the y-axis.Type the answer.
7 Question 7
Find the length of y = 34x from x = 0 to x = 4.Type the answer.
8 Question 8
Find the length of y = x48 + 1/(4x2) from x = 1 to x = 3.Type the answer.
9 Question 9
Find the surface area of y = 34x turned around the x-axis from x = 0 to x = 4.- A) S ≈ 4.712
- B) S ≈ 47.12
- C) S ≈ −47.12
- D) S ≈ 471.2
10 Question 10
Find the surface area of y = x33 turned around the x-axis from x = 0 to x = 2.Type the answer.
11 Question 11
Integrate ∫ x ex dxType the answer.
12 Question 12
Evaluate ∫ from 0 to 2 of x ex dx- A) 8.389
- B) 0.8389
- C) 8389
- D) 83.89
13 Question 13
Evaluate ∫ from 0 to π of sin2 x dx- A) 0.157
- B) 1.57
- C) 15.7
- D) 1570
14 Question 14
Evaluate ∫ from 0 to π of sin3 x dxType the answer.
15 Question 15
Integrate ∫ 1/(x2√(4 − x2)) dxType the answer.
16 Question 16
Evaluate ∫ from 0 to 4 of √(16 − x2) dxType the answer.
17 Question 17
Evaluate ∫ from 2 to 4 of 1/(x2 − 1) dx- A) 0.0294
- B) 0.294
- C) 1
- D) 2.94
18 Question 18
Evaluate ∫ from 1 to 2 of 3/(x2 + 3x) dx- A) 3
- B) 4.7
- C) 0.470
- D) 1
19 Question 19
Evaluate ∫ from 1 to ∞ of 1x2 dxType the answer.
20 Question 20
Evaluate ∫ from 0 to ∞ of 4e−2x dxType the answer.
21 Question 21
Find the limit of the sequence a_n = 5n2.- A) Converges
- B) Diverges
22 Question 22
Find the limit of the sequence a_n = n3 − 2n4n3 + 1.- A) Converges
- B) Diverges
23 Question 23
Does Σ n/(2n + 1) converge- A) Converges
- B) Diverges
24 Question 24
Does Σ (−1)n n2 + 12n2 converge- A) Converges
- B) Diverges
25 Question 25
Does Σ 1n2 converge- A) Converges
- B) Diverges
26 Question 26
Use the integral test on Σ 1n2/3- A) Converges
- B) Diverges
27 Question 27
Does Σ 1/(n2 + 3) converge- A) Converges
- B) Diverges
28 Question 28
Does Σ 3n − 1n3 + 1 converge- A) Converges
- B) Diverges
29 Question 29
Does Σ (−1)n+1/n converge- A) Converges
- B) Diverges
30 Question 30
Does Σ (−1)n 45n converge- A) Converges
- B) Diverges
31 Question 31
Does Σ 2nn! converge- A) Converges
- B) Diverges
32 Question 32
Does Σ (2n + 15n + 3)n converge- A) Converges
- B) Diverges
33 Question 33
Interval of convergence of Σ (x − 2)n/3nType the answer.
34 Question 34
Interval of convergence of Σ n!(x − 1)nType the answer.
35 Question 35
Maclaurin polynomial of degree 3 for exType the answer.
36 Question 36
Maclaurin polynomial of degree 4 for e−2xType the answer.
37 Question 37
x = t2, y = t3, find dy/dxType the answer.
38 Question 38
x = t2 − 2t, y = t3, find the slope at t = 2Type the answer.
39 Question 39
Find the area inside r = 3.- A) A ≈ 28.27
- B) A ≈ 282.7
- C) A ≈ 56.54
- D) 18π
40 Question 40
Find the area inside r = 4 + 2sin θ.Type the answer.