What is the main difference between the current line integral problem and the previous one discussed?

Evaluating Line Integrals and Vector Fields

Interactive Video
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Mathematics
•
11th Grade - University
•
Hard

Ethan Morris
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The current problem is in three dimensions.
The current problem involves a closed path.
The current problem uses a different vector field.
The current problem involves a non-closed path.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the parameterization of the curve used in this problem?
x = e^t, y = ln(t)
x = cos(t), y = sin(t)
x = t, y = t^2
x = sin(t), y = cos(t)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why can't the closed loop property be applied to this line integral?
Because the vector field is not defined.
Because the path is not closed.
Because the integral is in three dimensions.
Because the path is a straight line.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression for the vector field f in terms of i and j?
f = (x^2 - y^2)i + (2xy)j
f = (2xy)i + (x^2 + y^2)j
f = (x^2 + y^2)i + (2xy)j
f = (2xy)i + (x^2 - y^2)j
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean for a vector field to be conservative?
The field is space-dependent.
The field is path-independent.
The field is path-dependent.
The field is time-dependent.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the potential function F(x, y) for the vector field?
F(x, y) = x^3/3 + xy^2
F(x, y) = x^3/3 + y^3/3
F(x, y) = 2xy
F(x, y) = x^2 + y^2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the line integral evaluated for a conservative vector field?
By finding the divergence of the field.
By evaluating the potential function at the endpoints.
By integrating over the entire path.
By calculating the curl of the field.
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