Question

Consider the following region R and the vector field Bold Upper F.

a. Compute the​ two-dimensional divergence of the vector field.
b. Evaluate both integrals in​ Green's Theorem and check for consistency.
c. State whether the vector field is​ source-free. left angle negative 2 y comma 4 x right angle​; R is region bounded by yequals4 minus x squared and yequals0.
a. The​ two-dimensional divergence is 0.
b. Compute the integral of the divergence.
c. Integral from nothing to nothing
d. ModifyingBelow Integral from nothing to nothing With Upper R (StartFraction partial derivative f Over partial derivative x EndFraction plus StartFraction partial derivative g Over partial derivative y EndFraction )
e. A equals 0 Complete the line integral counterclockwise on the given​ curve, starting from the point ​(2​,0).
f. Represent the yequals4 minus x squared portion of the curve as the first integral and represent the yequals0 portion of the curve as the second integral.
g. ModifyingBelow Contour integral With Upper C f dy minus g dxequalsIntegral from negative 2 to 2 (nothing )dt plusIntegral from negative 2 to 2 (nothing )dt

Answer 1

Answer and Step-by-step explanation:

Workings and solutions to a, b, & c can be viewed in the snapshot below: