Please Answer the Following Questions (SHOW ALL WORK PLEASE)

1.

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. c. State whether the vector field is source-free. ( -y, - 6x) ; R is region bounded by y = 4 - x- and y = 0. a. The two-dimensional divergence is|15.4.29 Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $ (3x+ ex? ) dy- (4y' + sinhx) dx, where C is the boundary of the square with vertices (1, 5), (2, 5), (2, 6), and (1, 6). $ ( 3x + ex ? ) dy - (4y2 + sinh x) dx = [ (Type an exact answer.)