Vector Fields
Line Integrals
FTC of line integrals
Green's Theorem
100
What is a Function F that assigns to each point (x, y, z) in E a three-dimensional vector F(x, y, z)?
A vector field.
100
The definition of a line integral is the integral of f(x, y) * ds over a curve C. What does the ds equal?
The magnitude of r'(t).
100
What is a property of conservative vector fields?
Line intervals over conservative vector fields are path independent.
100
Fill in the blank:
Green's Theorem:
Let 
smooth, simple, closed
200
F(x, y, z) is a vector field in _______.
space
200
What does the line integral of a vector through a force field represent?
The work done.
200
Fill in the blank,
Let F be a vector field on an _____ and ______ region D. Then in P and Q have continuous partial deriveitives that are equal, then _____
Open, simply-connected, F is conservative.
200
Use Green's Theorem to evaluate the line integral along the given positively oriented curve.
The integral of xy2 dx + 2x2y dy over the curve, the triangle with vertices (0, 0), (2, 2), and (2, 4)
12
300
Match the following vector field with the graph: F(x, y) = 1/2(I + j)
(a)
(b)
(c)
a
300
Set up the line integral: F = y3 , C: x = t3, y = t, 0 < t< 2.
The integral from 0 to 2 of (t3)(9t4 + 1)1/2 * dt
300
Find a function f such that F is equal to the gradient of f.
F(x, y) =< x2, y2>
(x3 + y3)/3
300
Use Green's Theorem to evaluate the line integral along the given positively oriented curve.
The integral of cos(y) dx + x2sin(y) dy over the curve, the rectangle with vertices (0, 0), (5, 0), and (5, 2) and (0, 2)
30(1 - cos(2))
400
Determine the gradient vector field of f(x, y) = x2 -(1/4)y2
2x - (1/2)y
400
Evaluate the previous line integral.
32.32
400
Evaluate the previous integral of F * dr over the given curve C.
C is the arc of the parabola y = 2x2 from (-1, 2) to (2, 8)
171
400
FREE QUESTION
What is 0/0.