Consider the following region R and the vector field F 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. а. c. State whether the vector field is source free. (2ху"2 ; R is the region bounded by y = x(6- x) and y 0 F = - V a. The two-dimensional divergence is |0 b. Set up the integral over the region 6x(6-x) 0 dy dx Set up the line integral for the y= x(6 - x) boundary. dt 0
Consider the following region R and the vector field F 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. а. c. State whether the vector field is source free. (2ху"2 ; R is the region bounded by y = x(6- x) and y 0 F = - V a. The two-dimensional divergence is |0 b. Set up the integral over the region 6x(6-x) 0 dy dx Set up the line integral for the y= x(6 - x) boundary. dt 0
Consider the following region R and the vector field F 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. а. c. State whether the vector field is source free. (2ху"2 ; R is the region bounded by y = x(6- x) and y 0 F = - V a. The two-dimensional divergence is |0 b. Set up the integral over the region 6x(6-x) 0 dy dx Set up the line integral for the y= x(6 - x) boundary. dt 0
How do you set up the line integral for y=x(6-x) boundary?
Transcribed Image Text:Consider the following region R and the vector field F
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.
а.
c. State whether the vector field is source free.
(2ху"2
; R is the region bounded by y = x(6- x) and y 0
F =
- V
a. The two-dimensional divergence is |0
b. Set up the integral over the region
6x(6-x)
0 dy dx
Set up the line integral for the y= x(6 - x) boundary.
dt
0
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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