SOLVED: Consider the following region R and the vector field. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in the flux form of Green’s Theorem and check for c

Lec 23: Flux; normal form of Green’s theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 23: Flux; normal form of Green’s theorem | MIT 18.02 Multivariable Calculus, Fall 2007

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Consider the following region R and the vector field. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in the flux form of Green’s Theorem and check for consistency: State whether the vector field is source-free.
(2xyx^2 – y^2); R is the region bounded by y = x(2 – x) and y = 0.
a. The two-dimensional divergence is
b. Set up the integral over the region:
∫∫(2xyx^2 – y^2) dy dx
Set up the line integral for the y = x(2 – x) boundary.

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04:11

Consider the following region R and the vector field F_a: Compute the two-dimensional divergence of the vector field. b: Evaluate both integrals in the flux form of Green’s Theorem and check for consistency. c: State whether the vector field is source-free.

F = (8xy, x^2 – 4y^2); R is the region bounded by y = x(4 – x) and y = 0.

The two-dimensional divergence is

∇ · F = ∂(8xy)/∂x + ∂(x^2 – 4y^2)/∂y

Set up the integral over the region.

∫∫R ∇ · F dA

dy dx

05:32

17.4.29 – Setup & Solve

Consider the following region R and the vector field F. Compute the two-dimensional divergence of the vector field.

F = (2xy, x^2 – y)

R is the region bounded by y = x(2 – x) and y = 0.

a. The two-dimensional divergence is

b. Set up the integral over the region:

∫∫R 2x(2 – x) dy dx

Set up the line integral for the y = x(2 – x) boundary:

∫dt

02:43

Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green’s Theorem and check for consistency:

F = (-x, -y); R: x + y^2 < 9

03:08

Consider the following region R and the vector field F. Compute the two-dimensional divergence of the vector field. b: Evaluate both integrals in Green’s Theorem and check for consistency: F = (Zy, 4x); R is the triangle with vertices (0,0), (4,0), and (0,4): a. The two-dimensional divergence isb. Set up the integral over the region:∫∫ F · dA(Type exact answers)

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You are watching: SOLVED: Consider the following region R and the vector field. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in the flux form of Green’s Theorem and check for c. Info created by THVinhTuy selection and synthesis along with other related topics.

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