Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful. (4y + 3,4x"+5) . dr, where C is the boundary of the rectangle with vertices (0,0), (6,0), (6,4), and (0,4) $(4y + 3,4x2 + 5) . dr= (Type an exact answer.) CConsider the following region R and the vector eld F. a. Compute the twodimensional divergence of the vector eld. b. Evaluate both integrals in Green's Theorem and check for consistency. F= (2):,2y); R={x,y]: x2 +y259 a. The twodimensional divergence is E. (Type an exact answer.) b. Set up the integral over the region. Write the integral using polar coordinates. with r as the radius and B as the angle. DD l I [D r dr d9 {Type exact answers.) a Set up the line integral. Let the parameter be t= El, where B is the angle measured countercloclovise from the positive xaxis. I [D dt ((Type exact answers.) I] Evaluate these integrals and check for consistency. Select the correct choice below and ll in the answer oox[es} to complete your choice. (Type an exact answer.) 0 A- The integrals are not consistent. The double integral evaluates to I: O B- The integrals are consistent because they both evaluate to D. . but evaluating the line integrals and adding the results yields