Question: Please help with these two! Let D be the half-annulus given by {(r, 0) | 2 s r s 4, 0 s 0 S x),

Please help with these two!

Please help with these two! Let D be the half-annulus given by{(r, 0) | 2 s r s 4, 0 s 0 S

Let D be the half-annulus given by {(r, 0) | 2 s r s 4, 0 s 0 S x), and let F = (8y , -4x-), 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 (b) the flux of the vector field F outward from the region DLet D be the region between the circles C, and C, centered at the origin of radius 2 and 4, respectively. Assume C, and C, are oriented positively with respect to D. Use the extended version of Green's theorem for circulation to calculate -2x 4y -2x 4y dx + dy dx + dy. x 2+ x 2 + X 2+ y x 2 + C1

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