Green's theorem Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus-3/green-s-theorem/quiz/

1. 1

   Use Green's theorem on ∮ (x² − y) dx + (x + y²) dy around the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
   1. A) −2
   2. B) 1
   3. C) 2
   4. D) −1

2. 2

   Use Green's theorem on ∮ (y) dx + (2x) dy around the square 0 ≤ x ≤ 2, 0 ≤ y ≤ 2

   Answer: ____________________

3. 3

   Use Green's theorem on ∮ (x²) dx + (xy) dy around the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

   Answer: ____________________

4. 4

   Use Green's theorem on ∮ (2x − 3y) dx + (x + 4y) dy around the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

   Answer: ____________________

5. 5

   Use Green's theorem on ∮ (−2y) dx + (x) dy around the square 0 ≤ x ≤ 2, 0 ≤ y ≤ 2
   1. A) −12
   2. B) −2
   3. C) 6
   4. D) 12

6. 6

   Use Green's theorem on ∮ (xy) dx + (x²) dy around the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 1

   Answer: ____________________

7. 7

   Use Green's theorem on ∮ (x − y) dx + (x + y) dy around the rectangle 0 ≤ x ≤ 3, 0 ≤ y ≤ 2
   1. A) −12
   2. B) 4
   3. C) 12
   4. D) 1

8. 8

   Use Green's theorem on ∮ (−xy) dx + (x² + y) dy around the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 3

   Answer: ____________________

9. 9

   Use Green's theorem on ∮ (x² − 2y) dx + (3x + y²) dy around the rectangle 0 ≤ x ≤ 2, 0 ≤ y ≤ 1
   1. A) 3
   2. B) −2
   3. C) 10
   4. D) −10

10. 10

    Use Green's theorem on ∮ (y² − x) dx + (2xy + x²) dy around the rectangle 0 ≤ x ≤ 1, 0 ≤ y ≤ 2

    Answer: ____________________