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
A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by
= (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y-
direction.
(Use symbolic notation and fractions where needed.)
V. dS =
Sketch the vector field in the xy-plane.
F = -713
у
y
X
X
у
у
X
х
X
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