Exam 3 Graded
Student
Gia Patel
Total Points
pts
Question 1
Multiple Choice pts
1.1 Circumference pts
− 0 pts Correct! This integral represents the circumference of a circle of radius 3, which is 2πr = 6π
1.2 Conservative Vector Fields pts
− 0 pts Correct! The first and fourth choices are conservative.
1.3 Cones pts
− 2 pts (Chose z = r). Since it asks for spherical coordinates instead of cylindrical, it is ϕ = π/4.
1.4 FToLI pts
− 0 pts Correct! f (0, 0) − f (2, 1) = 0 − 4 = −4
Question 2
Concepts pts
2.1 Vector Field pts
− 0 pts Correct! This is the vector field ⟨y, 1⟩
2.2 Sign of Integral pts
− 0 pts Correct! The line integral will be positive.
2.3 Line Integral as Area pts
− 2 pts Incorrect. This is the scalar function line integral ∫C
f (x, y) ds.
, Question 3
Triple Integral pts
− 1 pt Wrong θ bounds. Should be −π/2 to π/2 or e.g. 3π/2 to 5π/2.
− 1 pt Wrong upper bound for ϕ. Should be π/4.
− 1 pt Wrong lower bound for ϕ. Should be 0.
− 1 pt Wrong ρ bounds. Should be 0 to 2.
Question 4
Scalar Line Integral pts
− 1 pt Error in bounds of integration. Should be 0 to π or something consistent with mistake above.
− 1 pt Error in final answer. Should be 512/3 or something consistent with mistake above.
Student
Gia Patel
Total Points
pts
Question 1
Multiple Choice pts
1.1 Circumference pts
− 0 pts Correct! This integral represents the circumference of a circle of radius 3, which is 2πr = 6π
1.2 Conservative Vector Fields pts
− 0 pts Correct! The first and fourth choices are conservative.
1.3 Cones pts
− 2 pts (Chose z = r). Since it asks for spherical coordinates instead of cylindrical, it is ϕ = π/4.
1.4 FToLI pts
− 0 pts Correct! f (0, 0) − f (2, 1) = 0 − 4 = −4
Question 2
Concepts pts
2.1 Vector Field pts
− 0 pts Correct! This is the vector field ⟨y, 1⟩
2.2 Sign of Integral pts
− 0 pts Correct! The line integral will be positive.
2.3 Line Integral as Area pts
− 2 pts Incorrect. This is the scalar function line integral ∫C
f (x, y) ds.
, Question 3
Triple Integral pts
− 1 pt Wrong θ bounds. Should be −π/2 to π/2 or e.g. 3π/2 to 5π/2.
− 1 pt Wrong upper bound for ϕ. Should be π/4.
− 1 pt Wrong lower bound for ϕ. Should be 0.
− 1 pt Wrong ρ bounds. Should be 0 to 2.
Question 4
Scalar Line Integral pts
− 1 pt Error in bounds of integration. Should be 0 to π or something consistent with mistake above.
− 1 pt Error in final answer. Should be 512/3 or something consistent with mistake above.
