Green's theorem Quiz
10 questions · easy to harder · Calculus 3 · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 4 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 the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Use Green's theorem on ∮ (x2 − y) dx + (x + y2) dy around the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1- A) −2
- B) 1
- C) 2
- D) −1
2 Question 2
Use Green's theorem on ∮ (y) dx + (2x) dy around the square 0 ≤ x ≤ 2, 0 ≤ y ≤ 2Type the answer.
3 Question 3
Use Green's theorem on ∮ (x2) dx + (xy) dy around the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1Type the answer.
4 Question 4
Use Green's theorem on ∮ (2x − 3y) dx + (x + 4y) dy around the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1Type the answer.
5 Question 5
Use Green's theorem on ∮ (−2y) dx + (x) dy around the square 0 ≤ x ≤ 2, 0 ≤ y ≤ 2- A) −12
- B) −2
- C) 6
- D) 12
6 Question 6
Use Green's theorem on ∮ (xy) dx + (x2) dy around the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 1Type the answer.
7 Question 7
Use Green's theorem on ∮ (x − y) dx + (x + y) dy around the rectangle 0 ≤ x ≤ 3, 0 ≤ y ≤ 2- A) −12
- B) 4
- C) 12
- D) 1
8 Question 8
Use Green's theorem on ∮ (−xy) dx + (x2 + y) dy around the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 3Type the answer.
9 Question 9
Use Green's theorem on ∮ (x2 − 2y) dx + (3x + y2) dy around the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 1- A) 3
- B) −2
- C) 10
- D) −10
10 Question 10
Use Green's theorem on ∮ (y2 − x) dx + (2xy + x2) dy around the rectangle 0 ≤ x ≤ 1, 0 ≤ y ≤ 2Type the answer.