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