Chapter 14.4, Problem 25E

Green’s Theorem, flux form Consider the following regions R and vector fields 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.

25.    F = (y, –3x); R is the region bounded by y = 4 – x² and y = 0.