Evaluating line integrals Evaluate the line integral ∫ C F ⋅ d r for the following vector fields F and curves C in two ways. a. By parameterizing C b. By using the Fundamental Theorem for line integrals, if possible 26. F = 〈 x , – y 〉; C is the square with vertices (±1, ±1) with counterclockwise orientation.
Evaluating line integrals Evaluate the line integral ∫ C F ⋅ d r for the following vector fields F and curves C in two ways. a. By parameterizing C b. By using the Fundamental Theorem for line integrals, if possible 26. F = 〈 x , – y 〉; C is the square with vertices (±1, ±1) with counterclockwise orientation.
Evaluating line integralsEvaluate the line integral
∫
C
F
⋅
d
r
for the following vector fieldsFand curves C in two ways.
a. By parameterizing C
b. By using the Fundamental Theorem for line integrals, if possible
26. F = 〈x, –y〉; C is the square with vertices (±1, ±1) with counterclockwise orientation.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Let (z, y, z)=
+ z ln (y + 2) be a scalar field.
Find the directional derivative of at P(2,2,-1) in the direction of the vector
12
4
Enter the exact value of your answer in the boxes below using Maple syntax.
Number
Sketch the vector field in the xy-plane.
F = -713
у
y
X
X
у
у
X
х
X
Describe the vector field by drawing some of its vectors.
F(x, y) = 5xi - 5yj
y
10
10
WebAssign Plot
10
10
10
10
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