3. [0/5 Points] DETAILS PREVIOUS ANSWERS Use Green's theorem for circulation to evaluate the line integral F - dir. F = ((xy2 + 4x), (3x + 2)) and C is the positively oriented boundary curve of the region bounded by y = 1, y = 2, y = -2x, and x = yz. Submit Answer Let D be the region shown in the figure that lies inside the square with vertices (+3, 0) and (0, #3) with boundary curve C,, and outside the square with edge length 1 that has boundary curve Cz. (0.3) C, (-3,0) (3,0) (0,-3) Let F = (P(x, y), Q(x, >). 0) be a continuously differentiable vector field. Use Greet theorem to compute the circulation of F around Cy if of F . adr = 210 and the z-component of the curl of F is equal to 4 on D 5. [2/4 Points] DETAILS PREVIOUS ANSWERS MY NOTES Let D be the half-annulus given by {(r, #) | 2 s rs 4, 0 s es x), and let F = (4y?, -3x?). with the boundary curve C of the region oriented counterclockwise. Use Green's theorems to compute the following- (a) the circulation of F around C 1792 (b) the flux of the vector field F outward from the region D 0 4. [0/5 Points] DETAILS PREVIOUS ANSWERS Use Lemma 14 from Section 7.5 to compute the volume of the solid that lies below the paraboloid z = 16 - x2 - y and above the plane z = 2