1.

Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise The circulation line integral of F = (41w2 ,4x:3 + y) where C is the boundary of {(x,y): O s y 5 sin x, 0 S x s 1:} CF-dFD (Type an exact answer, using 1: as needed.) Compute the curl of the following vector eld. F= (3x23 e!"2 ,2x2 3,:23'2 3x22 33" 2) The curl of F is (D) i + [D] j + (D) k. F = \\ 3xz3042 2X Z3042 3x z20yz > Curl F = K 2 ay 27 3x730y 2 x z ? ey 2 8 x z 2 042 ( 3x z 2 0 4 2 ) - 2 / 2x 2 3 0 42 ) - J 3 7 2 / 3 x 2 2 0 4 3 ) - 2 / 3x 7 3 (4 3) ? 2x + 1' 3 2 ( 2 X 7 3 0 4 3 ) .. - 2. ( 3x 2 3 0 4 3 ) ) = 7'7 ( 3 x z 3 ) ( 24) ( 0 4 3 ) - 6xz2042? = [ ' 7 6 x y z 2 - 6 x z 2 ) By 27 - J'7 32 2042 (1- 3x)} + K ' 7 2 2 3 0 4 2 6 xy z 3 0 4 27 6xz?( y -1 ) it ( 3 x - 1) 37 2042 /j + 22309 3 ( 1- 3 x4)