Green’s Theorem, circulation form Consider the following regions R and vector fields F . a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green’s Theorem and check for consistency. 17. F = 〈 2 y , − 2 x 〉 ; R is the region bounded by y = sin x and y = 0, for 0 ≤ x ≤ π
Green’s Theorem, circulation form Consider the following regions R and vector fields F . a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in Green’s Theorem and check for consistency. 17. F = 〈 2 y , − 2 x 〉 ; R is the region bounded by y = sin x and y = 0, for 0 ≤ x ≤ π
Green’s Theorem, circulation form Consider the following regions R and vector fields F.
a. Compute the two-dimensional curl of the vector field.
b. Evaluate both integrals in Green’s Theorem and check for consistency.
17. F =
〈
2
y
,
−
2
x
〉
; R is the region bounded by y = sin x and y = 0, for 0 ≤ x ≤ π
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.
Green’s Theorem, circulation form Consider the following regions R and vector fields F.a. Compute the two-dimensional curl of the vector field.b. Evaluate both integrals in Green’s Theorem and check for consistency.
F = ⟨2y, -2x⟩; R is the region bounded by y = sin x and y = 0, for 0 ≤ x ≤ π.
Let F=(9xy,7y,8z)=(9xy,7y,8z).The curl of F=(Is there a function f such that F=∇f=∇? (y/n)
Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero.
Positive
Positive
Zero
Zero
Negative
Positive
-
1.
University Calculus: Early Transcendentals (4th Edition)
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