
Understanding Line Integrals and Vector Fields

Interactive Video
•
Mathematics, Physics
•
11th Grade - University
•
Hard

Olivia Brooks
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of evaluating the line integral along the curve C?
To find the maximum value of the vector field
To find the length of the curve
To calculate the work done by the vector field on a particle
To determine the area enclosed by the curve
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the radius of the circle used in the problem?
5
3
4
2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the parametric equations for a circle centered at the origin?
x = r sec t, y = r csc t
x = r tan t, y = r cot t
x = r cos t, y = r sin t
x = r sin t, y = r cos t
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the x component of the vector function r(t) for the circle?
4 sin t
4 cos t
3 cos t
3 sin t
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the vector field F expressed as a function of t?
Using x = 4 sin t and y = 4 cos t
Using x = 3 sin t and y = 3 cos t
Using x = 4 cos t and y = 4 sin t
Using x = 3 cos t and y = 3 sin t
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the x component of r(t)?
4 sin t
-4 sin t
4 cos t
-4 cos t
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the dot product of F and r'(t)?
48 + 16 cos t sin t
32 + 16 cos t sin t
16 + 48 cos t sin t
16 + 32 cos t sin t
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